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Sample records for quadratic soliton compression

  1. Compression limits in cascaded quadratic soliton compression

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;

    2008-01-01

    Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency.......Cascaded quadratic soliton compressors generate under optimal conditions few-cycle pulses. Using theory and numerical simulations in a nonlinear crystal suitable for high-energy pulse compression, we address the limits to the compression quality and efficiency....

  2. Cascaded quadratic soliton compression at 800 nm

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Moses, Jeffrey;

    2007-01-01

    We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion.......We study soliton compression in quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

  3. Cascaded Quadratic Soliton Compression in Waveguide Structures

    DEFF Research Database (Denmark)

    Guo, Hairun

    The generation of few-cycle, high-intensity laser pulses is of great interests in a variety of research and application fields such as time-resolved spectroscopy, bio-chemical imaging with two-photon absorptions, medical treatment, material characterization, coherent supercontinuum generation...... and tera-hertz wave generation. Commercial pulsed lasers including the solid state system and the pulsed fiber laser have promised the generation of energetic femto-second pulses with the temporal duration around much more than tens of femto-seconds. Therefore, pulse compression technologies could be used...

  4. Cascaded quadratic soliton compression of high-power femtosecond fiber lasers in Lithium Niobate crystals

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, Jeffrey; Wise, Frank W.

    2008-01-01

    The output of a high-power femtosecond fiber laser is typically 300 fs with a wavelength around $\\lambda=1030-1060$ nm. Our numerical simulations show that cascaded quadratic soliton compression in bulk LiNbO$_3$ can compress such pulses to below 100 fs.......The output of a high-power femtosecond fiber laser is typically 300 fs with a wavelength around $\\lambda=1030-1060$ nm. Our numerical simulations show that cascaded quadratic soliton compression in bulk LiNbO$_3$ can compress such pulses to below 100 fs....

  5. Quadratic solitons as nonlocal solitons

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole

    2003-01-01

    We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...

  6. Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers

    DEFF Research Database (Denmark)

    Bache, Morten; Lægsgaard, Jesper; Bang, Ole;

    2007-01-01

    We investigate the possibility of using poled silica photonic crystal fibers for self-defocusing soliton compression with cascaded quadratic nonlinearities. Such a configuration has promise due to the desirable possibility of reducing the group-velocity mismatch. However, this unfortunately leads...... nonlinearity, and show that compression of nJ pulses to few-cycle duration is possible in such a fiber. A small amount of group-velocity mismatch optimizes the compression.......We investigate the possibility of using poled silica photonic crystal fibers for self-defocusing soliton compression with cascaded quadratic nonlinearities. Such a configuration has promise due to the desirable possibility of reducing the group-velocity mismatch. However, this unfortunately leads...

  7. Limits to compression with cascaded quadratic soliton compressors

    DEFF Research Database (Denmark)

    Bache, Morten; Bang, Ole; Krolikowski, Wieslaw;

    2008-01-01

    that it is theoretically possible to reach the single-cycle regime by compressing high-energy fs pulses for wavelengths λ = 1.0−1.3 μm in a β -barium-borate crystal, and it requires that the system is in the stationary regime, where the phase mismatch is large enough to overcome the detrimental GVM effects. however...

  8. Soliton compression to few-cycle pulses using quadratic nonlinear photonic crystal fibers: A design study

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper;

    2007-01-01

    We show theoretically that high-quality soliton compression from ~500 fs to ~10 fs is possible in poled silica photonic crystal fibers using cascaded (2):(2) nonlinearities. A moderate group-velocity mismatch optimizes the compression.......We show theoretically that high-quality soliton compression from ~500 fs to ~10 fs is possible in poled silica photonic crystal fibers using cascaded (2):(2) nonlinearities. A moderate group-velocity mismatch optimizes the compression....

  9. Impurity solitons with quadratic nonlinearities

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

    1998-01-01

    We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton p...

  10. Designing microstructured polymer optical fibers for cascaded quadratic soliton compression of femtosecond pulses

    DEFF Research Database (Denmark)

    Bache, Morten

    2009-01-01

    The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which in this study is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatch...

  11. Type-I cascaded quadratic soliton compression in lithium niobate: Compressing femtosecond pulses from high-power fiber lasers

    DEFF Research Database (Denmark)

    Bache, Morten; Wise, Frank W.

    2010-01-01

    using second-harmonic generation in a type-I phase-matching configuration. We find that because of competing cubic material nonlinearities, compression can only occur in the nonstationary regime, where group-velocity-mismatch–induced Raman-like nonlocal effects prevent compression to less than 100 fs...

  12. Solitons in quadratic nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families...

  13. Generating energetic few-cycle pulses at 800 nm using soliton compression with type 0 cascaded quadratic interaction in lithium niobate

    DEFF Research Database (Denmark)

    Bache, Morten; Zhou, Binbin; Chong, A.

    2010-01-01

    We show that ultra-short few-cycle pulses can be generated through soliton compression of energetic femtosecond pulses from a Ti:Sapphire regenerative amplifier. The compression relies on cascaded type 0 second-harmonic generation in mm-length lithium niobate crystals.......We show that ultra-short few-cycle pulses can be generated through soliton compression of energetic femtosecond pulses from a Ti:Sapphire regenerative amplifier. The compression relies on cascaded type 0 second-harmonic generation in mm-length lithium niobate crystals....

  14. Generating energetic few-cycle pulses at 800 nm using soliton compression with type 0 cascaded quadratic interaction in lithium niobate

    DEFF Research Database (Denmark)

    Bache, Morten; Zhou, Binbin; Chong, A.

    2010-01-01

    We show that ultra-short few-cycle pulses can be generated through soliton compression of energetic femtosecond pulses from a Ti:Sapphire regenerative amplifier. The compression relies on cascaded type 0 second-harmonic generation in mm-length lithium niobate crystals.......We show that ultra-short few-cycle pulses can be generated through soliton compression of energetic femtosecond pulses from a Ti:Sapphire regenerative amplifier. The compression relies on cascaded type 0 second-harmonic generation in mm-length lithium niobate crystals....

  15. Modulational stability and dark solitons in periodic quadratic nonlinear media

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2000-01-01

    We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....

  16. Dissipative quadratic solitons supported by a localized gain

    CERN Document Server

    Lobanov, Valery E; Malomed, Boris A

    2014-01-01

    We propose two models for the creation of stable dissipative solitons in optical media with the $\\chi^{(2)}$ (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized "hot spot", carrying the linear gain, is added, acting either on the FF component, or on the SH one. In both systems, we use numerical methods to find families of dissipative $\\chi^{(2)}$ solitons pinned to the "hot spot". The shape of the existence and stability domains may be rather complex. An existence boundary for the solitons, which corresponds to the guided mode in the linearized version of the systems, is obtained in an analytical form. The solitons demonstrate noteworthy features, such as spontaneous symmetry breaking (of spatially symmetric solitons) and bistability.

  17. Cascaded Soliton Compression of Energetic Femtosecond Pulses at 1030 nm

    DEFF Research Database (Denmark)

    Bache, Morten; Zhou, Binbin

    2012-01-01

    We discuss soliton compression with cascaded second-harmonic generation of energetic femtosecond pulses at 1030 nm. We discuss problems encountered with soliton compression of long pulses and show that sub-10 fs compressed pulses can be achieved.......We discuss soliton compression with cascaded second-harmonic generation of energetic femtosecond pulses at 1030 nm. We discuss problems encountered with soliton compression of long pulses and show that sub-10 fs compressed pulses can be achieved....

  18. Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: Generation of line and lump solitons from few-cycle input pulses

    CERN Document Server

    Leblond, Hervé; Mihalache, Dumitru; 10.1103/PHYSREVA.80.053812

    2011-01-01

    By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given.

  19. Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function

    DEFF Research Database (Denmark)

    Esbensen, B.K.; Bache, Morten; Krolikowski, W.;

    2012-01-01

    We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description t...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....

  20. Nonlinear compression of optical solitons

    Indian Academy of Sciences (India)

    M N Vinoj; V C Kuriakose

    2001-11-01

    In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.

  1. Evolution of Dark Spatial Soliton in Quasi-phase-matched Quadratic Media

    Institute of Scientific and Technical Information of China (English)

    WANG Fei-Yu; CHEN Xian-Feng; CHEN Yu-Ping; YANG Yi; XIA Yu-Xing

    2005-01-01

    We theoretically investigate the evolvement of dark spatial soliton with cascading quadratic nonlinearity in quasi-phase-matched second harmonic generation. It is shown that the dark solitary wave can propagate stably when background intensity is large enough, in which diffraction of beam can be balanced by the cascading quadratic nonlinearity. We also analyze the influence of phase-mismatch on the stability of dark soliton propagation.

  2. Soliton interaction in quadratic and cubic bulk media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole

    2000-01-01

    in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...

  3. A Quadratic Closure for Compressible Turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Futterman, J A

    2008-09-16

    We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

  4. Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities

    Institute of Scientific and Technical Information of China (English)

    LIN Ji; ZHAO Li-Na; LI Hua-Mei

    2011-01-01

    Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.

  5. Vectorial spatial solitons in bulk periodic quadratically nonlinear media

    Energy Technology Data Exchange (ETDEWEB)

    Panoiu, N-C [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States); Mihalache, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Mazilu, D [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Lederer, F [Institute of Solid State Theory and Theoretical Optics, Friedrich Schiller University Jena, Max-Wien-Platz 1, Jena, D-07743 (Germany); Osgood, R M Jr [Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027 (United States)

    2004-05-01

    We present a comprehensive analysis of the generation, propagation and characteristic properties of two-dimensional spatial solitons formed in quasi-phase-matched gratings through type-II vectorial interaction. By employing an averaging approach based on asymptotic expansion theory, we show that the dynamics of soliton propagation in the grating and their stability properties are strongly influenced by induced Kerr-like nonlinearities. Finally, through extensive numerical simulations, we verify the validity of our theoretical predictions.

  6. Observation of soliton compression in silicon photonic crystals

    Science.gov (United States)

    Blanco-Redondo, A.; Husko, C.; Eades, D.; Zhang, Y.; Li, J.; Krauss, T.F.; Eggleton, B.J.

    2014-01-01

    Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977

  7. Observation of soliton pulse compression in photonic crystal waveguides

    CERN Document Server

    Colman, P; Combrié, S; Sagnes, I; Wong, C W; De Rossi, A

    2010-01-01

    We demonstrate soliton-effect pulse compression in mm-long photonic crystal waveguides resulting from strong anomalous dispersion and self-phase modulation. Compression from 3ps to 580fs, at low pulse energies(~10pJ), is measured via autocorrelation.

  8. Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium

    Science.gov (United States)

    Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji

    2016-12-01

    The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164

  9. Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals

    CERN Document Server

    Liu, Xing; Guo, Hairun; Bache, Morten

    2015-01-01

    We show numerically that ultrashort self-defocusing temporal solitons colliding with a weak pulsed probe in the near-IR can convert the probe to the mid-IR. A near-perfect conversion efficiency is possible for a high effective soliton order. The near-IR self-defocusing soliton can form in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between $\\lambda=2.2-2.4~\\mu\\rm m$ as a resonant dispersive wave. This process relies on non-degenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation.

  10. Amplification and Compression of Ultrashort Fundamental Solitons in An Erbium-Doped Nonlinear Amplifying Fiber Loop Mirror

    Institute of Scientific and Technical Information of China (English)

    P.; K.; A.; Wai

    2003-01-01

    A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed device performs efficient high-quality amplification and compression of solitons.

  11. Electron-Acoustic Compressive Soliton and Electron Density Hole in Aurora

    Institute of Scientific and Technical Information of China (English)

    王德焴

    2003-01-01

    Electron-acoustic solitary waves have been studied in an electron-beam plasma system. It is found that the solution of compressive soliton only exists within a limited range of soliton velocity around the electron beam velocity. A compressive electron-acoustic soliton always accompanies with a cold electron density hole. This theoretical model is used to explain the ‘fast solitary wave' event observed by the FAST satellite in the midaltitude auroral zone.

  12. Improving Soliton Compression Quality with Cascaded Nonlinearities by Engineered Multi-section Quasi-phase-matching Design

    DEFF Research Database (Denmark)

    Zeng, Xianglong; Guo, Hairun; Zhou, Binbin

    2012-01-01

    In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced.......In few-cycle soliton generation with large compression factors using cascaded nonlinearities the pulse quality can be improved by engineering quasi-phase-matching structures. The soliton-induced mid-IR optical Cherenkov wave is also enhanced....

  13. Generating ultra-short energetic pulses with cascaded soliton compression in lithium niobate crystals

    DEFF Research Database (Denmark)

    Zhou, Binbin; Bache, Morten; Chong, A.;

    2010-01-01

    By launching energetic femtosecond pulses in a lithium niobate crystal, the phase mismatched second-harmonic generation process compresses the 50 fs input pulse at 1250 nm to 30 fs through a soliton effect.......By launching energetic femtosecond pulses in a lithium niobate crystal, the phase mismatched second-harmonic generation process compresses the 50 fs input pulse at 1250 nm to 30 fs through a soliton effect....

  14. Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals

    DEFF Research Database (Denmark)

    Liu, Xing; Zhou, Binbin; Guo, Hairun;

    2015-01-01

    in a quadratic nonlinear crystal (beta-barium borate) in the normal dispersion regime due to cascaded (phase-mismatched) second-harmonic generation, and the mid-IR converted wave is formed in the anomalous dispersion regime between. lambda = 2.2-2.4 mu m as a resonant dispersive wave. This process relies...... on nondegenerate four-wave mixing mediated by an effective negative cross-phase modulation term caused by cascaded soliton-probe sum-frequency generation. (C) 2015 Optical Society of America...

  15. Suppression of stimulated Brillouin scattering with phase modulator in soliton pulse compression

    Institute of Scientific and Technical Information of China (English)

    Bo Lü; Taorong Gong; Ming Chen; Muguang Wang; Tangjun Li; Genxiang Chen; Shuisheng Jian

    2009-01-01

    A phase modulator is employed in the scheme of soliton pulse compression with dispersion shifted fiber (DSF). Stimulated Brillouin scattering (SBS) effect, as a negative influence here, can be dramatically suppressed after optical phase modulation. The experimental result shows that the launched power required for high-order soliton pulse compression has been significantly increased by 11 dB under the condition of 100-MHz phase modulation. Accordingly, the experiment of picosecond pulse compression generated from electro-absorption sampling window (EASW) has also been implemented.

  16. Subpicosecond pulse compression in nonlinear photonic crystal waveguides based on the formation of high-order optical solitons

    Institute of Scientific and Technical Information of China (English)

    Chen Xiong-Wen; Lin Xu-Sheng; Lan Sheng

    2005-01-01

    We investigate by numerical simulation the compression of subpicosecond pulses in two-dimensional nonlinear photonic crystal (PC) waveguides. The compression originates from the generation of high-order optical solitons through the interplay of the huge group-velocity dispersion and the enhanced self-phase modulation in nonlinear PC waveguides.Both the formation of Bragg grating solitons and gap solitons can lead to efficient pulse compression. The compression factors under different excitation power densities and the optimum length for subpicosecond pulse compression have been determined. As a compressor, the total length of the nonlinear PC waveguide is only ten micrometres and therefore can be easily incorporated into PC integrated circuits.

  17. Compressive and rarefactive DIA solitons beyond the KdV limit

    Energy Technology Data Exchange (ETDEWEB)

    Mamun, A. A. [Abdus Salam International Centre for Theoretical Physics (Italy); Deeba, F., E-mail: farah.ju35@gmail.com [Jahangirnagar University, Department of Physics (Bangladesh)

    2012-04-15

    The modified Gardner equation (MGE), showing the existence of compressive and rarefactive dust-ion-acoustic (DIA) solitons in a nonplanar dusty plasma (containing inertial ions, Boltzmann electrons, and negatively charged stationary dust) beyond the KdV Korteweg-de Vries (KdV) limit, is derived and numerically solved. The basic features of the compressive and rarefactive cylindrical and spherical DIA solitons, which are found to exist beyond the KdV limit, i.e., exist for {mu} {approx} 2/3 (where {mu} = Z{sub n}n{sub d0}/n{sub i0}, z{sub d} is the number of electrons residing onto the dust grain surface, n{sub d0}(n{sub i0}) is the dust (ion) number density at equilibrium, and {mu} {approx} 2/3 means that {mu} is not equal to 2/3, but it is around 2/3) are identified. These solitons (which can be referred to as DIA Gardner solitons (DIA-GSs)) are completely different from the KdV solitons because {mu} = 2/3 corresponds to the vanishing of the nonlinear coefficient of the KdV equation, and {mu} {approx} 2/3 corresponds to extremely large amplitude KdV solitons for which the validity of the reductive perturbation method breaks down. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.

  18. Optical Solitons

    Science.gov (United States)

    Taylor, J. R.

    2005-08-01

    1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.

  19. Enhanced soliton-effect pulse compression by cross-phase modulation in optical fibers

    Institute of Scientific and Technical Information of China (English)

    曹文华; 刘颂豪

    2000-01-01

    A new method is proposed to enhance the soliton-effect compression of optical pulses. It consists of copropagating two optical pulses with close wavelengths in the anomalous group-velocity dispersion regime of single-mode fibers. Numerical simulations show that, as compared with the traditional single pulse compression method, cross-phase modulation can not only dramatically increase the compression ratio but also decrease the optimum fiber length. The effects of initial pulse-width mismatch, Raman self-scattering, and pulse walk-off on the pulse compression are also discussed.

  20. Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yu.S.

    1997-01-01

    We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the g......We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or chi((2))) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog...

  1. Quadratic vs cubic spline-wavelets for image representations and compression

    NARCIS (Netherlands)

    Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.

    1997-01-01

    The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary transform data. The use of semi-orthogonal quadratic spline wavelets allows one

  2. Quadratic vs cubic spline-wavelets for image representation and compression

    NARCIS (Netherlands)

    Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.

    1994-01-01

    The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary ransform data. The use of semi-orthogonal quadratic spline wavelets allows one t

  3. Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region

    CERN Document Server

    Jaramillo-Villegas, Jose A; Wang, Pei-Hsun; Leaird, Daniel E; Weiner, Andrew M

    2015-01-01

    A path within the parameter space of phase detuning and pump power is demonstrated in order to obtain a single cavity soliton (CS) with certainty in SiN microring resonators in the anomalous dispersion regime. Once the single CS state is reached, it is possible to continue a path to compress it, broadening the corresponding single FSR frequency Kerr comb. This behavior is first obtained by identifying the regions in the parameter space via numerical simulations of the Lugiato-Lefever equation (LLE), and second, defining a path from the stable modulation instability (SMI) region to the stable cavity solitons (SCS) region avoiding the chaotic and unstable regions.

  4. Low-energy Self-defocusing Soliton Compression at Optical Communication Wavelengths in Unpoled Lithium Niobate Ridge Waveguide

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin;

    2014-01-01

    Self-defocusing soliton compression supported by the cascaded phase-mismatched second-harmonic generation process is numerically demonstrated in unpoled lithium niobate ridge waveguides where nano-joule pulses are operated and quasi-phase-matching is unnecessary. The soliton range is 1100-1800 nm....

  5. Note on rarefactive and compressive ion-acoustic solitons in a plasma containing two ion species

    Science.gov (United States)

    McKenzie, J. F.; Verheest, F.; Doyle, T. B.; Hellberg, M. A.

    2005-10-01

    In a recent article the conditions for the existence of solitons in a plasma containing two ion species were analyzed within the framework of a fully nonlinear treatment. In particular, an upper limit for the critical collective Mach number (above which rarefactive solitons cease to exist) was obtained from the requirement that a charge neutral point in the rarefactive regime must be formed before the electron density, ne, experiences its "lid," i.e., where ne→0. Although this is a necessary condition it is not sufficient. In the present work a sufficient condition is derived by requiring that a rarefactive equilibrium point be reached before the limit is imposed by either the electron lid or the infinite compression of the second ion species. This requirement, along with the usual necessary condition for soliton formation, provides the parameter space window for the existence of rarefactive solitons. The analysis has also been generalized to include ions of finite mass of various charge for both the rarefactive and compressive cases.

  6. Solitons

    CERN Document Server

    Trullinger, SE; Pokrovsky, VL

    1986-01-01

    In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experime

  7. Deterministic single soliton generation and compression in microring resonators avoiding the chaotic region.

    Science.gov (United States)

    Jaramillo-Villegas, Jose A; Xue, Xiaoxiao; Wang, Pei-Hsun; Leaird, Daniel E; Weiner, Andrew M

    2015-04-20

    A path within the parameter space of detuning and pump power is demonstrated in order to obtain a single cavity soliton (CS) with certainty in SiN microring resonators in the anomalous dispersion regime. Once the single CS state is reached, it is possible to continue a path to compress it, broadening the corresponding single free spectral range (FSR) Kerr frequency comb. The first step to achieve this goal is to identify the stable regions in the parameter space via numerical simulations of the Lugiato-Lefever equation (LLE). Later, using this identification, we define a path from the stable modulation instability (SMI) region to the stable cavity solitons (SCS) region avoiding the chaotic and unstable regions.

  8. Sub-20 fs energetic near-IR pulses generated with cascaded soliton compression in short lithium niobate crystals

    DEFF Research Database (Denmark)

    Zhou, Binbin; Chong, Andy; Wise, Frank W.;

    2011-01-01

    We show experimentally that sub-20 fs near-infrared pulses can be generated through soliton compression of energetic femtosecond pulses.e compression relies on cascaded type-0 second-harmonic generation in a just 1 mm long lithium niobate crystal....

  9. Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing

    CERN Document Server

    Shechtman, Yoav; Szameit, Alexander; Segev, Mordechai

    2011-01-01

    We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.

  10. Characterization and compression of dissipative-soliton-resonance pulses in fiber lasers

    CERN Document Server

    Li, Daojing; Zhou, Junyu; Zhao, Luming; Tang, Dingyuan; Shen, Deyuan

    2016-01-01

    We report numerical and experimental studies of dissipative-soliton-resonance (DSR) in a fiber laser with a nonlinear optical loop mirror. The DSR pulse presents temporally a flat-top profile and a clamped peak power. Its spectrum has a rectangle profile with characteristic steep edges. It shows a unique behavior as pulse energy increases: The rectangle part of the spectrum is unchanged while the newly emerging spectrum sits on the center part and forms a peak. Experimental observations match well with the numerical results. Moreover, compression of the DSR pulses is both numerically and experimentally demonstrated for the first time. An experimentally obtained DSR pulse of 63 ps duration is compressed down to 760 fs, with low-intensity pedestals using a grating pair. Before being compressed to its narrowest width, the pulse firstly evolves into a cat-ear profile, and the corresponding autocorrelation trace shows a crown shape, which distinguishes itself from properties of other solitons formed in fiber laser...

  11. Large amplitude ion-acoustic rarefactive and compressive solitons and double layers in a dusty plasma with finite ion temperature

    Science.gov (United States)

    Jain, S. L.; Tiwari, R. S.; Mishra, M. K.

    2015-05-01

    Large amplitude ion-acoustic solitons and double layers are studied using Sagdeev's pseudo potential technique in a collisionless unmagnetized plasma consisting of hot and cold Maxwellian electrons, warm adiabatic ions, and heavily charged massive dust grains. It is found that for the selected set of plasma parameters, the system can support both solitons and double layers in the presence of negative as well as positive dust in the plasma. Further we have also investigated the ranges of parameters for simultaneous existence of both rarefactive and compressive supersonic solitons. The effects of dust concentration and ion temperature on the amplitude and Mach number of the double layer have also been studied. Our findings may be helpful in understanding the formation of non-linear structures, specially the solitons and double layers in space plasma, such as: in interstellar clouds, circumstellar clouds, planetary rings, comets, cometary tails, asteroid zones, auroral plasma, magnetospheric plasma, pulsars, and other astronomical environments and laboratory plasmas.

  12. Widely tunable mid-IR femtosecond resonant radiation induced by self-defocusing solitons in a quadratic nonlinear medium

    DEFF Research Database (Denmark)

    Zhou, Binbin; Liu, Xing; Guo, Hairun;

    2016-01-01

    We experimentally observe widely tunable mid-IR femtosecond pulses by resonant radiation, generated by direct three-wave-mixing from a soliton in PPLN. The poling pitch gives a parametrically tunable resonant radiation, a feature absent in Kerr media....

  13. Cochlear compression: effects of low-frequency biasing on quadratic distortion product otoacoustic emission.

    Science.gov (United States)

    Bian, Lin

    2004-12-01

    Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.

  14. Designing quadratic nonlinear photonic crystal fibers for soliton compression to few-cycle pulses

    DEFF Research Database (Denmark)

    Bache, Morten; Moses, Jeffrey; Lægsgaard, Jesper

    2007-01-01

    Second-harmonic generation (SHG) in the limit of large phase mismatch, given by Deltabeta=beta2-2beta1 effectively induces a Kerr-like nonlinear phase shift on the fundamental wave (FW). The phase mismatch determines the sign and magnitude of the effective Kerr nonlinearity, making large negative...

  15. Spatial solitons in nonlinear photonic crystals

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2000-01-01

    We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....

  16. Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

    DEFF Research Database (Denmark)

    Zhou, Binbin; Guo, Hairun; Bache, Morten

    2015-01-01

    and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...

  17. Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

    DEFF Research Database (Denmark)

    Zhou, Binbin; Guo, Hairun; Bache, Morten

    2015-01-01

    and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....

  18. Generating mid-IR octave-spanning supercontinua and few-cycle pulses with solitons in phase-mismatched quadratic nonlinear crystals

    DEFF Research Database (Denmark)

    Bache, Morten; Guo, Hairun; Zhou, Binbin

    2013-01-01

    of the promising crystals: in one case soliton pulse compression from 50 fs to 15 fs (1.5 cycles) at 3.0 μm is achieved, and at the same time a 3-cycle dispersive wave at 5.0 μm is formed that can be isolated using a long-pass filter. In another example we show that extremely broadband supercontinua can form......We discuss a novel method for generating octave-spanning supercontinua and few-cycle pulses in the important mid-IR wavelength range. The technique relies on strongly phase-mismatched cascaded second-harmonic generation (SHG) in mid-IR nonlinear frequency conversion crystals. Importantly we here...

  19. Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal

    CERN Document Server

    Zhou, B B; Bache, M

    2014-01-01

    Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO$_3$ cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband ($\\sim 1,000$ cm$^{-1}$) mid-IR pulses around $3.0~\\mu\\rm m$ are generated with excellent spatio-temporal pulse quality, having up to 10.5 $\\mu$J energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and la...

  20. Comment on "Electrostatic compressive and rarefactive shocks and solitons in relativistic plasmas occurring in polar regions of pulsar"

    Science.gov (United States)

    Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.

    2016-05-01

    The aim of this comment is to show the solution of the KdVB equation used by Shah et al. (Astrophys. Space Sci. 335:529-537, 2011, doi: 10.1007/s10509-011-0766-y) is not correct. So, the numerical results that are predicted in this manuscript should not be helpful for further investigations in a plasma laboratory. For this reason, we have employed the Bernoulli's equation method to obtain the correct form of analytical solution to this equation, which is appropriate for the study of electrostatic compressive and rarefactive shocks and solitons in relativistic plasmas occurring in polar regions of pulsar.

  1. IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

    Science.gov (United States)

    Kunze, Herb; La Torre, Davide; Lin, Jianyi

    2017-01-01

    We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

  2. Compressive and rarefactive dust-ion-acoustic Gardner solitons in a multi-component dusty plasma

    Energy Technology Data Exchange (ETDEWEB)

    Ema, S. A.; Ferdousi, M.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)

    2015-04-15

    The linear and nonlinear propagations of dust-ion-acoustic solitary waves (DIASWs) in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated theoretically. The linear properties are analyzed by using the normal mode analysis and the reductive perturbation method is used to derive the nonlinear equations, namely, the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. The basic features (viz., polarity, amplitude, width, etc.) of Gardner solitons (GS) are found to exist beyond the K-dV limit and these dust-ion-acoustic GS are qualitatively different from the K-dV and mK-dV solitons. It is observed that the basic features of DIASWs are affected by various plasma parameters (viz., electron nonextensivity, negative-to-positive ion number density ratio, electron-to-positive ion number density ratio, electron-to-positive ion temperature ratio, etc.) of the considered plasma system. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear structures and the characteristics of DIASWs propagating in both space and laboratory plasmas.

  3. Soliton-similariton switchable ultrafast fiber laser

    CERN Document Server

    Peng, Junsong; Guo, Pan; Gu, Zhaochang; Zou, Weiwen; Luo, Shouyu; Shen, Qishun

    2012-01-01

    For the first time, we demonstrated alternative generation of dispersion-managed (DM) solitons or similaritons in an all-fiber Erbium-doped laser. DM solitons or similaritons can be chosen to emit at the same output port by controlling birefringence in the cavity. The pulse duration of 87-fs for DM solitons and 248-fs for similaritons have been observed. For proof of similaritons, we demonstrate that the spectral width depends exponentially on the pump power, consistent with theoretical studies. Besides, the phase profile measured by a frequency-resolved optical gating (FROG) is quadratic corresponding to linear chirp. In contrast, DM solitons show non-quadratic phase profile.

  4. Dissipative soliton comb

    CERN Document Server

    Podivilov, Evgeniy V; Bednyakova, Anastasia E; Fedoruk, Mikhail P; Babin, Sergey A

    2016-01-01

    Dissipative solitons are stable localized coherent structures with linear frequency chirp generated in normal-dispersion mode-locked lasers. The soliton energy in fiber lasers is limited by the Raman effect, but implementation of intracavity feedback for the Stokes wave enables synchronous generation of a coherent Raman dissipative soliton. Here we demonstrate a new approach for generating chirped pulses at new wavelengths by mixing in a highly-nonlinear fiber of two frequency-shifted dissipative solitons, as well as cascaded generation of their clones forming a "dissipative soliton comb" in the frequency domain. We observed up to eight equidistant components in a 400-nm interval demonstrating compressibility from ~10 ps to ~300 fs. This approach, being different from traditional frequency combs, can inspire new developments in fundamental science and applications.

  5. Optical Vortex Solitons in Parametric Wave Mixing

    CERN Document Server

    Alexander, T J; Buryak, A V; Sammut, R A; Alexander, Tristram J.; Kivshar, Yuri S.; Buryak, Alexander V.; Sammut, Rowland A.

    2000-01-01

    We analyze two-component spatial optical vortex solitons supported by degenerate three- or four-wave mixing in a nonlinear bulk medium. We study two distinct cases of such solitons, namely, parametric vortex solitons due to phase-matched second-harmonic generation in a optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a bright localized ring-like mode of a fundamental frequency field.

  6. Spatiotemporal optical solitons

    Energy Technology Data Exchange (ETDEWEB)

    Malomed, Boris A [Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Mihalache, Dumitru [Department of Theoretical Physics, Institute of Atomic Physics, PO Box MG-6, Bucharest (Romania); Wise, Frank [Department of Applied Physics, 212 Clark Hall, Cornell University, Ithaca, NY 14853 (United States); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, Barcelona 08034 (Spain)

    2005-05-01

    In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic-cubic or cubic-quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose-Einstein condensates supported by full or low-dimensional optical lattices. (review article)

  7. Ion-acoustic solitons in multispecies spatially inhomogeneous plasmas

    Indian Academy of Sciences (India)

    Tarsem Singh Gill; Harvinder Kaur; Nareshpal Singh Saini

    2006-06-01

    Ion-acoustic solitons are investigated in the spatially inhomogeneous plasma having electrons-positrons and ions. The soliton characteristics are described by Korteweg-de Vries equation which has an additional term. The density and temperature of different species play an important role for the amplitude and width of the solitons. Numerical calculations show only the possibility of compressive solitons. Further, analytical results predict that the peak amplitude of soliton decreases with the decrease of density gradient. Soliton characteristics like peak amplitude and width are substantially different from those based on KdV theory for homogeneous plasmas.

  8. Solitons riding on solitons and the quantum Newton's cradle

    Science.gov (United States)

    Ma, Manjun; Navarro, R.; Carretero-González, R.

    2016-02-01

    The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.

  9. Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses Er3+-doped fiber amplifier

    Institute of Scientific and Technical Information of China (English)

    刘东峰; 陈国夫; 白晋涛; 王贤华

    2000-01-01

    Seed laser pulses with average power of 146 pW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration Er3+ -doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m Er3+ -doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.

  10. Quadratic choreographies

    CERN Document Server

    Ryckelynck, Philippe

    2011-01-01

    This paper addresses the classical and discrete Euler-Lagrange equations for systems of $n$ particles interacting quadratically in $\\mathbb{R}^d$. By highlighting the role played by the center of mass of the particles, we solve the previous systems via the classical quadratic eigenvalue problem (QEP) and its discrete transcendental generalization. The roots of classical and discrete QEP being given, we state some conditional convergence results. Next, we focus especially on periodic and choreographic solutions and we provide some numerical experiments which confirm the convergence.

  11. Temporal solitons in air

    Science.gov (United States)

    Voronin, A. A.; Zheltikov, A. M.

    2017-02-01

    Analysis of the group-velocity dispersion (GVD) of atmospheric air with a model that includes the entire manifold of infrared transitions in air reveals a remarkably broad and continuous anomalous-GVD region in the high-frequency wing of the carbon dioxide rovibrational band from approximately 3.5 to 4.2 μm where atmospheric air is still highly transparent and where high-peak-power sources of ultrashort midinfrared pulses are available. Within this range, anomalous dispersion acting jointly with optical nonlinearity of atmospheric air is shown to give rise to a unique three-dimensional dynamics with well-resolved soliton features in the time domain, enabling a highly efficient whole-beam soliton self-compression of such pulses to few-cycle pulse widths.

  12. Fusion arrest and collapse phenomena due to Kerr-nonlinearity in quadratic media

    DEFF Research Database (Denmark)

    Johansen, Steffen Kjær; Bang, Ole; Sørensen, Mads Peter

    2000-01-01

    Emphasizing collapse phenomena it is investigated to what extend the always present cubic nonlinearity affects the properties of soliton interaction in quadratic bulk media. An effective particle approach is applied and verified by numerical simulations....

  13. Vector Soliton Fiber Lasers

    CERN Document Server

    Zhang, Han

    2011-01-01

    Solitons, as stable localized wave packets that can propagate long distance in dispersive media without changing their shapes, are ubiquitous in nonlinear physical systems. Since the first experimental realization of optical bright solitons in the anomalous dispersion single mode fibers (SMF) by Mollenauer et al. in 1980 and optical dark solitons in the normal dispersion SMFs by P. Emplit et al. in 1987, optical solitons in SMFs had been extensively investigated. In reality a SMF always supports two orthogonal polarization modes. Taking fiber birefringence into account, it was later theoretically predicted that various types of vector solitons, including the bright-bright vector solitons, dark-dark vector solitons and dark-bright vector solitons, could be formed in SMFs. However, except the bright-bright type of vector solitons, other types of vector solitons are so far lack of clear experimental evidence. Optical solitons have been observed not only in the SMFs but also in mode locked fiber lasers. It has be...

  14. Soliton mechanics

    CERN Document Server

    Gunasekaran, Sharmila; Kunduri, Hari K

    2016-01-01

    The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have non-zero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This `first law of black hole and soliton mechanics' contains new intensive and extensive quantities associated to each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulae relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.

  15. Soliton mechanics

    Science.gov (United States)

    Gunasekaran, Sharmila; Hussain, Uzair; Kunduri, Hari K.

    2016-12-01

    The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess nontrivial 2-cycles (bubbles). Spacetimes containing such 2-cycles can have nonzero energy, angular momenta, and charge even in the absence of horizons. A mass variation formula has been established for spacetimes containing bubbles and possibly a black hole horizon. This "first law of black hole and soliton mechanics" contains new intensive and extensive quantities associated with each 2-cycle. We consider examples of such spacetimes for which we explicitly calculate these quantities and show how regularity is essential for the formulas relating them to hold. We also derive new explicit expressions for the angular momenta and charge for spacetimes containing solitons purely in terms of fluxes supporting the bubbles.

  16. Characteristic study of head-on collision of dust-ion acoustic solitons of opposite polarity with kappa distributed electrons

    Science.gov (United States)

    Parveen, Shahida; Mahmood, Shahzad; Adnan, Muhammad; Qamar, Anisa

    2016-09-01

    The head on collision between two dust ion acoustic (DIA) solitary waves, propagating in opposite directions, is studied in an unmagnetized plasma constituting adiabatic ions, static dust charged (positively/negatively) grains, and non-inertial kappa distributed electrons. In the linear limit, the dispersion relation of the dust ion acoustic (DIA) solitary wave is obtained using the Fourier analysis. For studying characteristic head-on collision of DIA solitons, the extended Poincaré-Lighthill-Kuo method is employed to obtain Korteweg-de Vries (KdV) equations with quadratic nonlinearities and investigated the phase shifts in their trajectories after the interaction. It is revealed that only compressive solitary waves can exist for the positive dust charged concentrations while for negative dust charge concentrations both the compressive and rarefactive solitons can propagate in such dusty plasma. It is found that for specific sets of plasma parameters, the coefficient of nonlinearity disappears in the KdV equation for the negative dust charged grains. Therefore, the modified Korteweg-de Vries (mKdV) equations with cubic nonlinearity coefficient, and their corresponding phase shift and trajectories, are also derived for negative dust charged grains plasma at critical composition. The effects of different plasma parameters such as superthermality, concentration of positively/negatively static dust charged grains, and ion to electron temperature ratio on the colliding soliton profiles and their corresponding phase shifts are parametrically examined.

  17. The generalized Kaup-Boussinesq equation: multiple soliton solutions

    Science.gov (United States)

    Wazwaz, Abdul-Majid

    2015-10-01

    In this work, we investigate the generalized two-field Kaup-Boussinesq (KB) equation. The KB equation possesses the cubic nonlinearity that distinguishes it from the Boussinesq equation that contains quadratic nonlinearity. We use the simplified form of Hirota's direct method to determine multiple soliton solutions and multiple singular soliton solutions for this equation. The study exhibits physical structures for a generalized water-wave model.

  18. Stable helical solitons in optical media

    Indian Academy of Sciences (India)

    Boris Malomed; G D Peng; P L Chu; Isaac Towers; Alexander V Buryak; Rowland A Sammut

    2001-11-01

    We present a review of new results which suggest the existence of fully stable spinning solitons (self-supporting localised objects with an internal vorticity) in optical fibres with self-focusing Kerr (cubic) nonlinearity, and in bulk media featuring a combination of the cubic self-defocusing and quadratic nonlinearities. Their distinctive difference from other optical solitons with an internal vorticity, which were recently studied in various optical media, theoretically and also experimentally, is that all the spinning solitons considered thus far have been found to be unstable against azimuthal perturbations. In the first part of the paper, we consider solitons in a nonlinear optical fibre in a region of parameters where the fibre carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of application to communication systems, this opens the way to doubling the number of channels carried by a fibre. Besides that, these solitons are objects of fundamental interest. To fully examine their stability, it is crucially important to consider collisions between them, and their collisions with fundamental solitons, in (ordinary or hollow) optical fibres. We introduce a system of coupled nonlinear Schrödinger equations for the fundamental and helical modes with nonstandard values of the cross-phase-modulation coupling constants, and show, in analytical and numerical forms, results of collisions between solitons carried by the two modes. In the second part of the paper, we demonstrate that the interaction of the fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing Kerr nonlinearity, gives rise to the first ever example of completely stable spatial ring-shaped solitons with intrinsic vorticity. The stability is demonstrated both by direct simulations and by analysis of linearized equations.

  19. Nontopological solitons

    CERN Document Server

    Wilets, Lawrence

    1989-01-01

    Successful modeling of quantum chromodynamics with a relativistic quark-soliton field theory has been developed over the past decade. As introduced by R Freidberg and T D Lee, the foundation of the model involves the chromodielectric properties of the physical vacuum, which yield absolute color confinement. The model allows for the consistent calculation of the dynamics of hadrons and hadronic reactions. The book summarizes and expands upon the extensive literature on the subject, concentrating on the Friedberg-Lee model and variations thereof. New results and future directions are included. T

  20. Parametric localized modes in quadratic nonlinear photonic structures

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;

    2001-01-01

    We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....

  1. Solvable quadratic Lie algebras

    Institute of Scientific and Technical Information of China (English)

    ZHU; Linsheng

    2006-01-01

    A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.

  2. Induced Kerr effects and self-guided beams in quasi-phase-matched quadratic media [CBC4

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Bang, Ole; Kivshar, Yuri S.

    1997-01-01

    We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons......We show that quasi-phase-matching of quadratic media induces Kerr effects, such as self- and cross-phase modulation, and leads to the existence of a novel class of solitary waves, QPM-solitons...

  3. Soliton formation in hollow-core photonic bandgap fibers

    DEFF Research Database (Denmark)

    Lægsgaard, Jesper

    2009-01-01

    of an approximate scaling relation is tested. It is concluded that compression of input pulses of several ps duration and sub-MW peak power can lead to a formation of solitons with ∼100 fs duration and multi-megawatt peak powers. The dispersion slope of realistic hollow-core fibers appears to be the main obstacle......The formation of solitons upon compression of linearly chirped pulses in hollow-core photonic bandgap fibers is investigated numerically. The dependence of soliton duration on the chirp and power of the input pulse and on the dispersion slope of the fiber is investigated, and the validity...

  4. Multiple-octave spanning mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

    CERN Document Server

    Zhou, Binbin

    2016-01-01

    Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystal like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal pumped in the mid-IR gives multiple-octave spanning supercontinua. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed (covering 1.6-$7.0~\\mu$m). The results were recorded in a commercially available crystal LiInS$_2$ pumped in the 3-$4~\\mu$m range, but other mid-IR crystals ...

  5. Vector Lattice Vortex Solitons

    Institute of Scientific and Technical Information of China (English)

    WANG Jian-Dong; YE Fang-Wei; DONG Liang-Wei; LI Yong-Ping

    2005-01-01

    @@ Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth Vo. For small Vo, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large Vo, this case is inversed. If Vo is large enough, both the types of such solitons are stable.

  6. Solitonic Gateless Computing

    Science.gov (United States)

    2006-01-29

    Jakubowski, and R. Squier, “Collisions of two solitons in an arbitrary number of coupled nonlinear Schrodinger equations ”, Physical Review Letters 90...on Nonlinear Evolution Equations and Wave Phenomena, Athens, Georgia, April 11-14, 2005. 89. D. N. Christodoulides, “ Discrete solitons in...Solitons for signal processing applications: 1. Navigating discrete solitons in two-dimensional nonlinear waveguide array networks: Among

  7. Introduction to solitons

    Indian Academy of Sciences (India)

    Miki Wadati

    2001-11-01

    As an introduction to the special issue on nonlinear waves, solitons and their significance in physics are reviewed. The soliton is the first universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.

  8. CHARACTERIZATION AND MODELING OF SOLITON TRANSMISSION AT 2.5 GB/S OVER 200 KM

    Directory of Open Access Journals (Sweden)

    KHALID A. S. AL-KHATEEB

    2010-09-01

    Full Text Available Soliton characteristics and soliton transmission have been simulated using a VPI simulator. Simulation was also used to construct and study a soliton communication system. Near soliton pulses emitted by an actively mode-locked laser is then compressed in a dispersion-compensating fiber (DCF to produce solitons. The effects of non-linearity and active pre-chirping of mode-locked laser diode sources were also investigated. Assessment on a modeled system using real data shows that propagation over 250 km at 2.5 Gb/s in standard fibers with 20 ps pulse widths is possible in the 1550 nm wavelength range.

  9. Multicolor Bound Soliton Molecule

    CERN Document Server

    Luo, Rui; Lin, Qiang

    2015-01-01

    We show a new class of bound soliton molecule that exists in a parametrically driven nonlinear optical cavity with appropriate dispersion characteristics. The composed solitons exhibit distinctive colors but coincide in time and share a common phase, bound together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor bound soliton molecule shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which may open up a great avenue towards versatile generation and manipulation of multi-octave spanning phase-locked Kerr frequency combs, with great potential for applications in frequency metrology, optical frequency synthesis, and spectroscopy.

  10. Classically Isospinning Hopf Solitons

    CERN Document Server

    Battye, Richard A

    2013-01-01

    We perform full 3-dimensional numerical relaxations of isospinning Hopf solitons with Hopf charge up to 8 in the Skyrme-Faddeev model with mass terms included. We explicitly allow the soliton solution to deform and to break the symmetries of the static configuration. It turns out that the model with its rich spectrum of soliton solutions, often of similiar energy, allows for transmutations, formation of new solution types and the rearrangement of the spectrum of minimal-energy solitons in a given topological sector when isospin is added. We observe that the shape of isospinning Hopf solitons can differ qualitatively from that of the static solution. In particular the solution type of the lowest energy soliton can change. Our numerical results are of relevance for the quantization of the classical soliton solutions.

  11. Interactions of breathers and solitons of the extended Korteweg de Vries equation

    Science.gov (United States)

    Shek, C. M.; Grimshaw, R. H. J.; Ding, E.

    2005-11-01

    A popular model for the evolution of weakly nonlinear, weakly dispersive waves in the ocean is the extended Korteweg -- de Vries equation (eKdV), which incorporates both quadratic and cubic nonlinearities. The case of positive cubic nonlinearity allows for both solitons of elevation and depression, as well as breathers (pulsating modes). Multi-soliton solutions are computed analytically, and will yield expressions for breather-soliton interactions. Both the soliton and breather will retain their identities after interactions, but suffer phase shifts. However, the details of the interaction process will depend on the polarity of the interacting soliton, and have been investigated by a computer algebra software. This highly time dependent motion during the interaction process is important in nonlinear science and physical oceanography. As the dynamics of the current and an evolving internal oceanic tide can be modeled by eKdV, this knowledge is relevant to the temporal and spatial variability observed in the oceanic internal soliton fields.

  12. STABILITY OF BRIGHT SCREENING-PHOTOVOLTAIC SPATIAL SOLITONS

    Institute of Scientific and Technical Information of China (English)

    LIU JING-SONG; ZHANG DU-YING; LIANG CHANG-HONG

    2000-01-01

    We present a theoretical analysis of the stability of screening-photovoltaic (SP) spatial solitons in biased photovoltaic-photorefractive materials in the case of neglecting the loss of the material and the effect of diffusion.When an incident optical beam is a SP soliton, this beam propagates along a linear path with its shape kept unchanged.When the maximum amplitude, width and functional form of an incident optical beam are slightly different from those of a SP soliton, the beam reshapes itself and tries to evolve into a solitary wave after a short distance. That is, these SP solitons are stable against small perturbations. However, optical beams that significantly differ from SP soliton solutions tend to experience larger cycles of compression and expansion, and their maximum amplitudes oscillate with propagation distances. The larger the perturbations, the stronger the oscillation.

  13. Self compression and raman soliton generation in a photonic crystal fibre of 100-fs pulses produced by a diode-pumped Yb-doped oscillator

    DEFF Research Database (Denmark)

    Druon, F.; Sanner, N.; Lucas-Leclin, G.

    2003-01-01

    We present the use of a photonic crystal fiber to straightforwardly compress ultrashort pulses from a diode-pumped ytterbium laser emitting around 1 m. 75-fs pulse generation and a large 11.3-m tunability for sub-100-fs pulses is reported.......We present the use of a photonic crystal fiber to straightforwardly compress ultrashort pulses from a diode-pumped ytterbium laser emitting around 1 m. 75-fs pulse generation and a large 11.3-m tunability for sub-100-fs pulses is reported....

  14. Statistical foundation of the fluid analogue of the soliton formalism

    Science.gov (United States)

    Tchen, C. M.

    1986-01-01

    A fully nonlinear analysis is used to develop a general soliton formalism for the description of the nonlinear evolution of soliton fluctuations in both plasmas and classical fluids. From the Navier-Stokes equations for plasmas and compressible fluids of two scales, two equations for the propagation of density waves are derived. A fast soliton field is spontaneously created by rarefaction, and a slow density wave modulates the field intensity as a ponderomotive force. Constitutive properties are demonstrated using a Lagrangian-kinetic formalism of the fluctuation-dissipation theory.

  15. Enhanced Transmission Stability of Polarization Solitons in Birefringent Fibres with an Optical Phase Conjugator

    Institute of Scientific and Technical Information of China (English)

    陈伟成; 谢嘉宁; 路洪; 徐文成

    2003-01-01

    An optical phase conjugator is used to enhance transmission stability of polarization solitons in highly birefringent fibres. Two polarization solitons form a breather in fibres with low birefringence firstly and the optical phase conjugator is used to make the spectra of polarization solitons converse, which results in the fact that the polarization soliton along the fast axis is compressed due to the strengthened self-phase modulation effect. Two polarization solitons are compressed further due to the cross-phase modulation effect. The enhanced nonlinear effects make the central peak frequencies of two polarization solitons shift to the larger range in opposite directions so that they trap each other fully to suppress the effect of birefringence.

  16. Experimental studies of high order soliton compression effect and gain characteristics in femtosecond laser pulses E3+r-doped fiber amplifier

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Seed laser pulses with average power of 146 μW and pulse duration of 480 fs were amplified to 14.5 mW. The pulse duration was compressed to 260 fs using 6 m high concentration E3+r-doped fiber under forward pumping. The amplified signal pulse energy was 0.691 nJ (corresponding to a peak power of 2 657.7 W) and the repetition rate was 20.84 MHz. Spectrum breakup was observed simultaneously. The spectrum of pulses amplified by 3 m E3+r-doped fiber remains a single peak under different pump power. The amplified pulse duration was compressed abnormally with the increasing pump power using the backward pumping; that is, the amplified pulses were compressed with the increasing pump power under low pump power. When the pump power reached 38 mW, the shortest amplified pulse duration was 309 fs. With further increase in pump power, the amplified pulses began broadening, accompanied by a single peak spectrum under different pump power.

  17. The Versatile Soliton

    CERN Document Server

    Filippov, Alexandre T

    2010-01-01

    If you have not already heard about solitons, you will sooner or later encounter them. The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The main concepts and results of theoretical physics related to solitons can be ex

  18. Evolution of Bright Screening-photovoltaic Spatial Optical Solitons

    Institute of Scientific and Technical Information of China (English)

    LIU Jinsong

    2001-01-01

    A numerical analysis of the dynamical evolution of bright screening-photovoltaic (SP) spatial solitons in biased photovoltaic-photorefractive materials in the case of neglecting the material loss and the diffusion is presented. When an incident optical beam is a bright SP soliton, the beam propagates along a linear path with its shape kept unchanged. When the incident optical beam is slightly different from a bright SP soliton, the beam reshapes itself and tries to evolve into a bright SP soliton after a short distance. However, when the incident optical beam is significantly different from a SP bright soliton, the beam cannot evolve into a stable bright SP soliton, and tends to experience periodic compression and expansion. For a low-intensity input beam, the wave experiences a periodic process of compression first and then expansion during the initial part of the cycle. For a high-intensity input beam, however, the wave will initially diffract and then experiences compression during the cycle.

  19. Unexpected Behavior on Nonlinear Tunneling of Chirped Ultrashort Soliton Pulse in Non-Kerr Media with Raman Effect

    Science.gov (United States)

    Rajan, M. S. Mani

    2016-08-01

    In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.

  20. Invited Article: Multiple-octave spanning high-energy mid-IR supercontinuum generation in bulk quadratic nonlinear crystals

    Science.gov (United States)

    Zhou, Binbin; Bache, Morten

    2016-08-01

    Bright and broadband coherent mid-IR radiation is important for exciting and probing molecular vibrations. Using cascaded nonlinearities in conventional quadratic nonlinear crystals like lithium niobate, self-defocusing near-IR solitons have been demonstrated that led to very broadband supercontinuum generation in the visible, near-IR, and short-wavelength mid-IR. Here we conduct an experiment where a mid-IR crystal is pumped in the mid-IR. The crystal is cut for noncritical interaction, so the three-wave mixing of a single mid-IR femtosecond pump source leads to highly phase-mismatched second-harmonic generation. This self-acting cascaded process leads to the formation of a self-defocusing soliton at the mid-IR pump wavelength and after the self-compression point multiple octave-spanning supercontinua are observed. The results were recorded in a commercially available crystal LiInS2 pumped in the 3-4 μm range with 85 fs 50 μJ pulse energy, with the broadest supercontinuum covering 1.6-7.0 μm. We measured up 30 μJ energy in the supercontinuum, and the energy promises to scale favorably with an increased pump energy. Other mid-IR crystals can readily be used as well to cover other pump wavelengths and target other supercontinuum wavelength ranges.

  1. The quadratic Fock functor

    CERN Document Server

    Accardi, Luigi

    2009-01-01

    We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.

  2. Quadratic eigenvalue problems.

    Energy Technology Data Exchange (ETDEWEB)

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  3. Contributions to the application of solitons in optical communication systems

    Science.gov (United States)

    Mostofi, Amir

    The field of optical soliton communication systems has made remarkable progress in the recent past, and yet it is still growing in many different directions. This thesis is essentially a collection of a variety of numerical investigations that were conducted in an attempt to introduce some new ideas in this area, as well as shed further light on certain already considered issues. The thesis consists of the following general topics: (1)A new multilevel TDM soliton transmission system has been proposed, where each channel transmits its data in the form of picosecond fundamental solitons of a unique amplitude. At the receiver, the pulses are compressed to the subpicosecond level, and separated in the wavelength domain, by taking advantage of the different Raman-induced self-wavelength shifts experienced. Through numerical simulations and noise analyses, the feasibility of the system has been investigated. (2)The use of trains of unequal- amplitude solitons for improving the undoing of soliton interactions in periodically amplified systems using optical phase conjugation has been considered and compared with the case of phase-alternation between neighbouring solitons. (3)It has been found that dispersion-decreasing fibres with the commonly used hyperbolic dispersion profile are not always a good option for near adiabatic, pedestal-free compression of soliton pulses. In fact, they appear to be inferior to some other simple dispersion profiles, such as linear, Gaussian, and exponential, particularly when compression of subpicosecond solitons is involved. (4)The fact that nonlinear couplers with constant core separation cannot be fabricated with very long lengths has been considered to pose a problem for reliable observation of soliton propagation in them. The nonconstancy of the core separation has been modelled in this thesis in terms of random fluctuations in the coupling coefficient, and the effects of these fluctuations on both dynamical switching and static

  4. Geometry of Ricci Solitons

    Institute of Scientific and Technical Information of China (English)

    Huai-Dong CAO

    2006-01-01

    Ricci solitons are natural generalizations of Einstein metrics on one hand, and are special solutions of the Ricci flow of Hamilton on the other hand. In this paper we survey some of the recent developments on Ricci solitons and the role they play in the singularity study of the Ricci flow.

  5. Soliton absorption spectroscopy

    CERN Document Server

    Kalashnikov, V L

    2010-01-01

    We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width using the novel perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively modelocked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurement in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improving of the sensitivity and spectroscopic accuracy making the soliton absorption spectroscopy a promising novel measurement technique.

  6. Stokes Soliton in Optical Microcavities

    CERN Document Server

    Yang, Qi-Fan; Yang, Ki Youl; Vahala, Kerry

    2016-01-01

    Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical-potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The di...

  7. Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal

    DEFF Research Database (Denmark)

    Zhou, Binbin; Bache, Morten

    2015-01-01

    We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited...... in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phasematching wavelengths due to degenerate four-wave mixing to the soliton. We also...... observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations....

  8. Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal.

    Science.gov (United States)

    Zhou, Binbin; Bache, Morten

    2015-09-15

    We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phase-matching wavelengths due to degenerate four-wave mixing to the soliton. We also observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations.

  9. On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities

    Indian Academy of Sciences (India)

    R S Kaushal; Ranjit Kumar; Awadhesh Prasad

    2006-08-01

    Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.

  10. Multistage quadratic stochastic programming

    Science.gov (United States)

    Lau, Karen K.; Womersley, Robert S.

    2001-04-01

    Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.

  11. Ion-acoustic Gardner Solitons in electron-positron-ion plasma with two-electron temperature distributions

    Science.gov (United States)

    Rehman, Momin A.; Mishra, M. K.

    2016-01-01

    The ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons, and two temperature distribution of electrons have been studied. Using reductive perturbation method, Korteweg-de Vries (K-dV), the modified K-dV (m-KdV), and Gardner equations are derived for the system. The soliton solution of the Gardner equation is discussed in detail. It is found that for a given set of parameter values, there exists a critical value of β=Tc/Th, (ratio of cold to hot electron temperature) below which only rarefactive KdV solitons exist and above it compressive KdV solitons exist. At the critical value of β, both compressive and rarefactive m-KdV solitons co-exist. We have also investigated the soliton in the parametric regime where the KdV equation is not valid to study soliton solution. In this region, it is found that below the critical concentration the system supports rarefactive Gardner solitons and above it compressive Gardner solitons are found. The effects of temperature ratio of two-electron species, cold electron concentration, positron concentration on the characteristics of solitons are also discussed.

  12. Role of Magnetosonic Solitons in Perpendicular Collisionless Shock Reformation

    Science.gov (United States)

    Gueroult, Renaud; Ohsawa, Yukiharu; Fisch, Nathaniel J.

    2017-03-01

    The nature of the magnetic structure arising from ion specular reflection in shock compression studies is examined by means of 1D particle-in-cell simulations. Propagation speed, field profiles, and supporting currents for this magnetic structure are shown to be consistent with a magnetosonic soliton. Coincidentally, this structure and its evolution are typical of foot structures observed in perpendicular shock reformation. To reconcile these two observations, we propose, for the first time, that shock reformation can be explained as the result of the formation, growth, and subsequent transition to a supercritical shock of a magnetosonic soliton. This argument is further supported by the remarkable agreement found between the period of the soliton evolution cycle and classical reformation results. This new result suggests that the unique properties of solitons can be used to shed new light on the long-standing issue of shock nonstationarity and its role on particle acceleration.

  13. Compactons versus solitons

    Indian Academy of Sciences (India)

    Paulo E G Assis; Andreas Fring

    2010-06-01

    We investigate whether the recently proposed $\\mathcal{PT}$-symmetric extensions of generalized Korteweg–de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable.

  14. Multidimensional Localized Solitons

    CERN Document Server

    Boiti, M; Martina, L; Boiti, Marco

    1993-01-01

    Abstract: Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the main results obtained in the last five years thanks to the renewed interest in soliton theory due to this discovery. The theoretical tools needed to understand the unexpected richness of behaviour of multidimensional localized solitons during their mutual scattering are furnished. Analogies and especially discrepancies with the unidimensional case are stressed.

  15. Helmholtz algebraic solitons

    Energy Technology Data Exchange (ETDEWEB)

    Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

    2010-02-26

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  16. Bipolar solitons of the focusing nonlinear Schrödinger equation

    Science.gov (United States)

    Liu, Zhongxuan; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun

    2016-11-01

    The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.

  17. Bipolar solitons of the focusing nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Zhongxuan, E-mail: 13237379393@163.com; Feng, Qi; Lin, Chengyou; Chen, Zhaoyang; Ding, Yingchun, E-mail: dingyc@mail.buct.edu.cn

    2016-11-15

    The focusing nonlinear Schrödinger equation (NLSE) is a universal model for studying solitary waves propagation in nonlinear media. The NLSE is especially important in understanding how solitons on a condensate background (SCB) appear from a small perturbation through modulation instability. We study theoretically the one- and two-soliton solutions of the NLSE in presence of a condensate by using the dressing method. It is found that a class of bipolar elliptically polarized solitons with the choice of specific parameters in the one- and two-soliton solutions. Collisions among these solitons are studied by qualitative analysis and graphical illustration. We also generalize the concept of the quasi-Akhmediev breather to the bipolar solitons and show how it can be used for wave profile compression down to the extremely short duration. Our results extend previous studies in this area of the SCB and play an important role in the theory of freak wave.

  18. Quantum Soliton Evaporation

    CERN Document Server

    Villari, Leone Di Mauro; Biancalana, Fabio; Conti, Claudio

    2016-01-01

    We have very little experience of the quantum dynamics of the ubiquitous nonlinear waves. Observed phenomena in high energy physics are perturbations to linear waves, and classical nonlinear waves, like solitons, are barely affected by quantum effects. We know that solitons, immutable in classical physics, exhibit collapse and revivals according to quantum mechanics. However this effect is very weak and has never been observed experimentally. By predicting black hole evaporation Hawking first introduced a distinctly quantum effect in nonlinear gravitational physics.Here we show the existence of a general and universal quantum process whereby a soliton emits quantum radiation with a specific frequency content, and a temperature given by the number of quanta, the soliton Schwarzschild radius, and the amount of nonlinearity, in a precise and surprisingly simple way. This result may ultimately lead to the first experimental evidence of genuine quantum black hole evaporation. In addition, our results show that bla...

  19. Color chiral solitons

    CERN Document Server

    Novozhilov, V Yu; Novozhilov, Victor; Novozhilov, Yuri

    2002-01-01

    We discuss specific features of color chiral solitons (asymptotics, possibility of confainment, quantization) at example of isolated SU(2) color skyrmions, i.e. skyrmions in a background field which is the vacuum field forming the gluon condensate.

  20. Temporal dark polariton solitons

    CERN Document Server

    Kartashov, Yaroslav V

    2016-01-01

    We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid dark and anti-dark light-matter solitons. Such temporal solitons exist due to interplay between repulsive excitonic nonlinearity and giant group velocity dispersion arising in the vicinity of excitonic resonance. Such fully conservative states do not require external pumping to counteract losses and form continuous families parameterized by the power-dependent phase shift and velocity of their motion. Dark solitons are stable in the considerable part of their existence domain, while anti-dark solitons are always unstable. Both families exist outside forbidden frequency gap of the linear system.

  1. Gravitating $\\sigma$ Model Solitons

    OpenAIRE

    Kim, Yoonbai; Moon, Sei-Hoon

    1998-01-01

    We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes with...

  2. Nonlocal incoherent solitons

    DEFF Research Database (Denmark)

    Krolikowski, Wieslaw; Bang, Ole; Wyller, John

    2004-01-01

    We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.......We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....

  3. Phase Statistics of Soliton

    OpenAIRE

    Ho, Keang-Po

    2003-01-01

    The characteristic function of soliton phase jitter is found analytically when the soliton is perturbed by amplifier noise. In additional to that from amplitude jitter, the nonlinear phase noise due to frequency and timing jitter is also analyzed. Because the nonlinear phase noise is not Gaussian distributed, the overall phase jitter is also non-Gaussian. For a fixed mean nonlinear phase shift, the contribution of nonlinear phase noise from frequency and timing jitter decreases with distance ...

  4. The soliton stars evolution

    CERN Document Server

    Bednarek, I; Bednarek, Ilona; Manka, Ryszard

    1996-01-01

    The evolution of a soliton star filled with fermions is studied in the framework of general relativity. Such a system can be described by the surface tension $\\sigma$, the bag constant $B$, and the fermion number density affects the spacetime inside the soliton. Whether it is described by Friedman or de Sitter metric depends on the prevailing parameter. The whole spacetime is devided by the surface of the soliton into the false vacuum region inside the soliton and the true vacuum region outside, the latter being described by the Schwarzschild line element. The aim of this paper is to study the equations of motion of the domain wall in two cases. In the first case the de Sitter metric describes the interior in the first case, and in the second case it is replaced by the Friedman metric. In both of them the Schwarzschild metric is outside the soliton. From the analysis of obtained equations one can draw conclusions concerning further evolution of a soliton star.

  5. Soliton-plasma nonlinear dynamics in mid-IR gas-filled hollow-core fibers

    DEFF Research Database (Denmark)

    Habib, Selim; Markos, Christos; Bang, Ole

    2017-01-01

    We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 mu m. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity...... dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self...

  6. Semidefinite programming for quadratically constrained quadratic programs

    Science.gov (United States)

    Olkin, Julia A.; Titterton, Paul J., Jr.

    1995-06-01

    We consider the linear least squares problem subject to multiple quadratic constraints, which is motivated by a practical application in controller design. We use the techniques of convex optimization, in particluar, interior-point methods for semi-definite programming. We reduce a quasi-convex potential function. Each iteration requires calculating a primal and dual search direction and minimizing along the plane defined by these search directions. The primal search direction requires solving a least squares problem whose matrix is composed of a block- Toeplitz portion plus other structured matrices. We make use of Kronecker products and FFTs to greatly reduce the calculation. In addition, the matrix updates and matrix inverses in the plane search are actually low-rank updates to structured matrices so we are able to further reduce the flops required. Consequently, we can design controllers for problems of considerable size.

  7. Interaction of spatial photorefractive solitons

    DEFF Research Database (Denmark)

    Królikowski, W.; Denz, C.; Stepken, A.

    1998-01-01

    beam or the complete annihilation of some of them, depending on the relative phase of the interacting beams. In the case of mutually incoherent solitons, we show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal...... that a soliton pair may experience both attractive and repulsive forces; depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions....

  8. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  9. On Convex Quadratic Approximation

    NARCIS (Netherlands)

    den Hertog, D.; de Klerk, E.; Roos, J.

    2000-01-01

    In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

  10. On Quadratic Differential Forms

    NARCIS (Netherlands)

    Willems, J.C.; Trentelman, H.L.

    1998-01-01

    This paper develops a theory around the notion of quadratic differential forms in the context of linear differential systems. In many applications, we need to not only understand the behavior of the system variables but also the behavior of certain functionals of these variables. The obvious cases w

  11. Aspects of Quadratic Gravity

    CERN Document Server

    Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

    2016-01-01

    We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

  12. Influence of superthermal electrons on propagation of arbitrary amplitude ion-acoustic solitons in a plasma with negative ions

    Directory of Open Access Journals (Sweden)

    Z Ebne Abbasi

    2013-03-01

    Full Text Available   Investigation of ion acoustic solitons in three component plasma including positive and negative ions and Maxwellian electrons shows that negative to positive relative ion density plays a critical role so that by changing ν over the range of 0<ν<1 compressive or rarefactive solitons will propagate. In this paper, it is shown that due to the superthermal electrons, there are three domains for ν so that in the first one only compressive solitons are allowed, in the second one compressive and rarefactive solitons coexist together and in the third one only rarefactive solitons are observed. The results from sagdeev potential in weak nonlinear region are in good agreement with analytic results obtained from KdV equation.

  13. The volume of a soliton

    Energy Technology Data Exchange (ETDEWEB)

    Adam, C., E-mail: adam@fpaxp1.usc.es [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Haberichter, M. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Wereszczynski, A. [Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków (Poland)

    2016-03-10

    There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.

  14. Transverse stability of Kawahara solitons

    DEFF Research Database (Denmark)

    Karpman, V.I.

    1993-01-01

    The transverse stability of the planar solitons described by the fifth-order Korteweg-de Vries equation (Kawahara solitons) is studied. It is shown that the planar solitons are unstable with respect to bending if the coefficient at the fifth-derivative term is positive and stable if it is negative...

  15. The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

    Directory of Open Access Journals (Sweden)

    Feng-Tao He

    2013-01-01

    Full Text Available We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton’s dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1 if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton’s width increases, while its amplitude and wave velocity reduce. (2 If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton’s width increases, while its amplitude and the wave velocity reduce.

  16. Ion-acoustic solitons in negative ion plasma with two-electron temperature distributions

    Energy Technology Data Exchange (ETDEWEB)

    Mishra, M. K.; Tiwari, R. S.; Chawla, J. K. [Department of Physics, University of Rajasthan, Jaipur-302004 (India)

    2012-06-15

    Ion-acoustic solitons in a warm positive and negative ion species with different masses, concentrations, and charge states with two electron temperature distributions are studied. Using reductive perturbation method, Korteweg de-Vries (KdV) and modified-KdV (m-KdV) equations are derived for the system. The soliton solution of the KdV and m-KdV equations is discussed in detail. It is found that if the ions have finite temperatures, then there exist two types of modes, namely slow and fast ion-acoustic modes. It is also investigated that the parameter determining the nature of soliton (i.e., whether the system will support compressive or rarefactive solitons) is different for slow and fast modes. For the slow mode, the parameter is the relative temperature of the two ion species; whereas for the fast mode, it is the relative concentration of the two ion species. At a critical concentration of negative ions, both compressive and rarefactive solitons coexist. The amplitude and width of the solitons are discussed in detail at critical concentration for m-KdV solitons. The effect of the relative temperature of the two-electron and cold-electron concentration on the characteristics of the solitons are also discussed.

  17. Hidden conic quadratic representation of some nonconvex quadratic optimization problems

    NARCIS (Netherlands)

    Ben-Tal, A.; den Hertog, D.

    2014-01-01

    The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma

  18. Annihilation Solitons and Chaotic Solitons for the (2+1)-Dimensional Breaking Soliton System

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    By means of an improved mapping method and a variable separation method, a scries of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) to the (2+1)-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.

  19. Numerical Exploration of Soliton Creation

    CERN Document Server

    Lamm, Henry

    2013-01-01

    We explore the classical production of solitons in the easy axis O(3) model in 1+1 dimensions, for a wide range of initial conditions that correspond to the scattering of small breathers. We characterize the fractal nature of the region in parameter space that leads to soliton production and find certain trends in the data. We identify a tension in the initial conditions required for soliton production - low velocity incoming breathers are more likely to produce solitons, while high velocity incoming breathers provide momentum to the final solitons and enable them to separate. We find new "counter-spinning" initial conditions that can alleviate some of this tension.

  20. Oscillating solitons in nonlinear optics

    Indian Academy of Sciences (India)

    Lin Xiao-Gang; Liu Wen-Jun; Lei Ming

    2016-03-01

    Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.

  1. Solitons in nonlinear lattices

    CERN Document Server

    Kartashov, Yaroslav V; Torner, Lluis

    2010-01-01

    This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...

  2. Soliton driven angiogenesis

    Science.gov (United States)

    Bonilla, L. L.; Carretero, M.; Terragni, F.; Birnir, B.

    2016-08-01

    Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.

  3. Extended gcd of quadratic integers

    CERN Document Server

    Miled, Abdelwaheb

    2010-01-01

    Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.

  4. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...

  5. Stokes solitons in optical microcavities

    Science.gov (United States)

    Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry

    2017-01-01

    Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.

  6. Soliton crystals in Kerr resonators

    CERN Document Server

    Cole, Daniel C; Del'Haye, Pascal; Diddams, Scott A; Papp, Scott B

    2016-01-01

    Solitons are pulses that propagate without spreading due to a balance between nonlinearity and dispersion (or diffraction), and are universal features of systems exhibiting these effects. Solitons play an important role in plasma physics, fluid dynamics, atomic physics, biology, and optics. In the context of integrated photonics, bright dissipative cavity solitons in Kerr-nonlinear resonators are envisioned to play an important role in next-generation communication, computation, and measurement systems. Here we report the discovery of soliton crystals in Kerr resonators-collectively ordered ensembles of co-propagating solitons with discrete allowed temporal separations. Through analysis of optical spectra, we identify a complicated but discrete space of interacting soliton configurations, including crystals exhibiting vacancies (Schottky defects), shifted pulses (Frenkel defects), and superstructure. Time-domain characterization of the output-coupled soliton pulse train directly confirms our inference of the ...

  7. Accessible solitons of fractional dimension

    Energy Technology Data Exchange (ETDEWEB)

    Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2016-05-15

    We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

  8. Gravitating $\\sigma$ Model Solitons

    CERN Document Server

    Kim, Y; Kim, Yoonbai; Moon, Sei-Hoon

    1998-01-01

    We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.

  9. Semiclassical geons as solitonic black hole remnants

    Energy Technology Data Exchange (ETDEWEB)

    Lobo, Francisco S.N. [Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa (Portugal); Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: flobo@cii.fc.ul.pt, E-mail: gonzalo.olmo@csic.es, E-mail: drubiera@fisica.ufpb.br2 [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia - CSIC. Universidad de Valencia, Burjassot-46100, Valencia (Spain)

    2013-07-01

    We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to ∼ 16 units of charge. Though these objects are locally indistinguishable from spherically symmetric, massive electric (or magnetic) charges, they turn out to be sourceless geons containing a wormhole generated by the electromagnetic field. Our results are obtained by interpreting semiclassical corrections to Einstein's theory in the first-order (Palatini) formalism, which yields second-order equations and avoids the instabilities of the usual (metric) formulation of quadratic gravity. We also discuss the potential relevance of these solutions for primordial black holes and the dark matter problem.

  10. Solitons on the supermembrane

    NARCIS (Netherlands)

    Bergshoeff, Eric; Townsend, Paul K.

    1999-01-01

    Energy bounds are derived for planar and compactified M2-branes in a hyper-Kähler background. These bounds are saturated, respectively, by lump and Q-kink solitons, which are shown to preserve half the worldvolume supersymmetry. The Q-kinks have a dual IIB interpretation as strings that migrate bet

  11. Self-trapped optical beams: Spatial solitons

    Indian Academy of Sciences (India)

    Andrey A Sukhorukov; Yuri S Kivshar

    2001-11-01

    We present a brief overview of the basic concepts of the theory ofspatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.

  12. Periodic modulations controlling Kuznetsov–Ma soliton formation in nonlinear Schrödinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Tiofack, C.G.L., E-mail: glatchio@yahoo.fr [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); Coulibaly, S.; Taki, M. [Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille (France); De Bièvre, S.; Dujardin, G. [Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille (France); Équipe-Projet Mephysto, INRIA Lille-Nord Europe (France)

    2017-06-28

    We analyze the exact Kuznetsov–Ma soliton solution of the one-dimensional nonlinear Schrödinger equation in the presence of periodic modulations satisfying an integrability condition. We show that, in contrast to the case without modulation, the Kuznetsov–Ma soliton develops multiple compression points whose number, shape and position are controlled both by the intensity of the modulation and by its frequency. In addition, when this modulation frequency is a rational multiple of the natural frequency of the Kuznetsov–Ma soliton, a scenario similar to a nonlinear resonance is obtained: in this case the spatial oscillations of the Kuznetsov–Ma soliton's intensity are periodic. When the ratio of the two frequencies is irrational, the soliton's intensity is a quasiperiodic function. A striking and important result of our analysis is the possibility to suppress any component of the output spectrum of the Kuznetsov–Ma soliton by a judicious choice of the amplitude and frequency of the modulation. - Highlights: • Exact Kuznetsov–Ma soliton solution in presence of periodic coefficients is obtained. • The multiple compression points of the solution are studied. • The quasi-periodicity of the solution is discussed. • The possibility to suppress any component of the spectrum is analyzed.

  13. Formation of quasiparallel Alfven solitons

    Science.gov (United States)

    Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.

    1992-01-01

    The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.

  14. Efficient supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching

    CERN Document Server

    Guo, Hairun; Steinert, Michael; Setzpfandt, Frank; Pertsch, Thomas; Chung, Hung-ping; Chen, Yen-Hung; Bache, Morten

    2014-01-01

    Efficient supercontinuum generation (SCG) requires excitation of solitons at the pump laser wavelength. Quadratic nonlinear waveguides may support an effective self-defocusing nonlinearity so solitons can directly be generated at common ultrafast laser wavelengths without any waveguide dispersion engineering. We here experimentally demonstrate efficient SCG in a standard lithium niobate (LN) waveguide without using quasi-phase matching (QPM). By using femtosecond pumps with wavelengths in the $1.25-1.5 \\mu\\rm m$ range, where LN has normal dispersion and thus supports self-defocusing solitons, octave-spanning SCG is observed. An optimized mid-IR waveguide design is expected to support even broader spectra. The QPM-free design reduces production complexity, allows longer waveguides, limits undesired spectral resonances and effectively allows using nonlinear crystals where QPM is inefficient or impossible. This result is important for mid-IR SCG, where QPM-free self-defocusing waveguides in common mid-IR nonline...

  15. Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media

    Directory of Open Access Journals (Sweden)

    Roxana Savastru

    2012-01-01

    Full Text Available We present the propagation of optical beams and the properties of one-dimensional (1D spatial solitons (“bright” and “dark” in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1 a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.

  16. Influence of air pressure on soliton formation in hollow-core photonic bandgap fibers

    DEFF Research Database (Denmark)

    Lægsgaard, Jesper; Roberts, Peter John

    2009-01-01

    Abstract Soliton formation during dispersive compression of chirped few-picosecond pulses at the microjoule level in a hollow-core photonic bandgap (HC-PBG) fiber is studied by numerical simulations. Long-pass filtering of the emerging frequency-shifted solitons is investigated with the objective...... at high powers. This allows a scaling of the output pulse energy toward the microjoule level. © 2009 Optical Society of America...

  17. Relativistic solitons and superluminal signals

    Energy Technology Data Exchange (ETDEWEB)

    Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, Monterotondo, Rome 00015 (Italy)]. E-mail: solitone@yahoo.it

    2005-02-01

    Envelope solitons in the weakly nonlinear Klein-Gordon equation in 1 + 1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier wave, on the contrary in the second case solitons always move with the group velocity of the carrier wave, but now this velocity is greater than the light speed. Superluminal signals are then possible in classical relativistic nonlinear field equations.

  18. Exact periodic and solitonic states of the spinor condensates in a uniform external potential

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Zhi-Hai [School of Physics and Electronics, Yancheng Teachers University, Yancheng 224051 (China); Yang, Shi-Jie, E-mail: yangshijie@tsinghua.org.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)

    2016-08-15

    We propose a method to analytically solve the one-dimensional coupled nonlinear Gross–Pitaevskii equations which govern the motion of the spinor Bose–Einstein condensates. In a uniform external potential, several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates for the Hamiltonian comprising the kinetic energy, the linear and the quadratic Zeeman energies. Real solutions take the form of composite soliton trains. Complex solutions correspond to the mass counter-flows as well as spin currents. These solutions are general that contains neither approximations nor constraints on the system parameters.

  19. Lump and lump-soliton solutions to the (2+1) -dimensional Ito equation

    Science.gov (United States)

    Yang, Jin-Yun; Ma, Wen-Xiu; Qin, Zhenyun

    2017-06-01

    Based on the Hirota bilinear form of the (2+1) -dimensional Ito equation, one class of lump solutions and two classes of interaction solutions between lumps and line solitons are generated through analysis and symbolic computations with Maple. Analyticity is naturally guaranteed for the presented lump and interaction solutions, and the interaction solutions reduce to lumps (or line solitons) while the hyperbolic-cosine (or the quadratic function) disappears. Three-dimensional plots and contour plots are made for two specific examples of the resulting interaction solutions.

  20. Weakly deformed soliton lattices

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)

    1990-12-01

    In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).

  1. A CLASS OF QUADRATIC HAMILTONIAN SYSTEMS UNDER QUADRATIC PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    丰建文; 陈士华

    2001-01-01

    This paper deals with a class of quadratic Hamiltonian systems with quadratic perturbation. The authors prove that if the first order Melnikov function M1(h) = 0 and the second order Melnikov function M2(h) ≡ 0, then the origin of the Hamiltonian system with small perturbation is a center.

  2. Solitons: mathematical methods for physicists

    Energy Technology Data Exchange (ETDEWEB)

    Eilenberger, G.

    1981-01-01

    The book is a self-contained introduction to the theory of solitons. The Korteweg-de Vries equation is investigated and the inverse scattering transformation is treated in detail. Techniques are applied to the Toda lattice and solutions of the sine-Gordon equation. An introduction to the thermodynamics of soliton systems is given. (KAW)

  3. Solitons in spiraling Vogel lattices

    CERN Document Server

    Kartashov, Yaroslav V; Torner, Lluis

    2012-01-01

    We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.

  4. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

    2005-01-01

    that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...

  5. Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

    Science.gov (United States)

    Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

    2017-02-01

    We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

  6. Solitons in generalized Galileon theories

    Science.gov (United States)

    Carrillo González, Mariana; Masoumi, Ali; Solomon, Adam R.; Trodden, Mark

    2016-12-01

    We consider the existence and stability of solitons in generalized Galileons, scalar-field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons exist in a single Galileon theory using an argument invoking the existence of zero modes for the perturbations. Here we analyze the applicability of this argument to generalized Galileons and discuss how this may be avoided by having potential terms in the energy functional for the perturbations or by including time dependence. Given the presence of potential terms in the Lagrangian for the perturbations, we find that stable, static solitons are not ruled out in conformal and (anti-)de Sitter Galileons. For the case of Dirac-Born-Infeld and conformal Galileons, we find that solitonic solutions moving at the speed of light exist, the former being stable and the latter unstable if the background soliton satisfies a certain condition.

  7. Solitons in generalized galileon theories

    CERN Document Server

    Carrillo-Gonzalez, Mariana; Solomon, Adam R; Trodden, Mark

    2016-01-01

    We consider the existence and stability of solitons in generalized galileons, scalar field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons exist in a single galileon theory using an argument invoking the existence of zero modes for the perturbations. Here we analyze the applicability of this argument to generalized galileons and discuss how this may be avoided by having potential terms in the energy functional for the perturbations, or by including time dependence. Given the presence of potential terms in the Lagrangian for the perturbations, we find that stable, static solitons are not ruled out in conformal and (A)dS galileons. For the case of DBI and conformal galileons, we find that solitonic solutions moving at the speed of light exist, the former being stable and the latter unstable if the background soliton satisfies a certain condition.

  8. Thermophoresis of an antiferromagnetic soliton

    Science.gov (United States)

    Kim, Se Kwon; Tchernyshyov, Oleg; Tserkovnyak, Yaroslav

    2015-07-01

    We study the dynamics of an antiferromagnetic soliton under a temperature gradient. To this end, we start by phenomenologically constructing the stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid of the fluctuation-dissipation theorem. We then derive the Langevin equation for the soliton's center of mass by the collective coordinate approach. An antiferromagentic soliton behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of solitons, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a soliton. The diffusion coefficient is inversely proportional to a small damping constant α , which can yield a drift velocity of tens of m/s under a temperature gradient of 1 K/mm for a domain wall in an easy-axis antiferromagnetic wire with α ˜10-4 .

  9. Breather soliton dynamics in microresonators

    CERN Document Server

    Yu, Mengjie; Okawachi, Yoshitomo; Griffith, Austin G; Luke, Kevin; Miller, Steven A; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L

    2016-01-01

    The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems with a localized temporal structure that exhibits oscillatory behavior. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here, we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation in good agreement with the numerical simulations. Our study presents experimental confirmation of the stability diagram of dissipative cavity solitons predicted by the Lugiato-Lefever equation and is importance to understandin...

  10. Solitons and quasi-periodic behaviors in an inhomogeneous optical fiber

    Science.gov (United States)

    Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei; Feng, Yu-Jie

    2017-01-01

    In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation for the attosecond pulses in an inhomogeneous optical fiber is studied. With the aid of auxiliary functions, we obtain the variable-coefficient Hirota bilinear equations and corresponding integrable constraints. Under those constraints, we obtain the Lax pair, conservation laws, one-, two- and three-soliton solutions via the Hirota method and symbolic computation. Soliton structures and interactions are discussed: (1) For the one soliton, we discuss the influence of the group velocity dispersion term α(x) and fifth-order dispersion term δ(x) on the velocities and structures of the solitons, where x is the normalized propagation along the fiber, and derive a constraint contributing to the stationary soliton; (2) For the two solitons, we analyze the interactions between them with different values of α(x) and δ(x), and derive the quasi-periodic formulae for three cases of the bound states: When α(x) and δ(x) are the linear functions of x, quasi-periodic attraction and repulsion lead to the redistribution of the energy of the two solitons, and ratios among the quasi-periods are derived; When α(x) and δ(x) are the quadratic functions of x, the ratios among them are also obtained; When α(x) and δ(x) are the periodic functions of x, bi-periodic phenomena are obtained; (3) For the three solitons, including the parabolic, cubic, periodic and stationary structures, interactions among them with different values of the α(x) and δ(x) are presented.

  11. Generation of bright soliton through the interaction of black solitons

    CERN Document Server

    Losano, L; Bazeia, D

    2001-01-01

    We report on the possibility of having two black solitons interacting inside a silica fiber that presents normal group-velocity dispersion, to generate a pair of solitons, a vector soliton of the black-bright type. The model obeys a pair of coupled nonlinear Schr\\"odinger equations, that follows in accordance with a Ginzburg-Landau equation describing the anisotropic XY model. We solve the coupled equations using a trial-orbit method, which plays a significant role when the Schr\\"odinger equations are reduced to first order differential equations.

  12. Chirped Dissipative Solitons

    CERN Document Server

    Kalashnikov, Vladimir L

    2010-01-01

    The analytical theory of chirped dissipative soliton solutions of nonlinear complex Ginzburg-Landau equation is exposed. Obtained approximate solutions are easily traceable within an extremely broad range of the equation parameters and allow a clear physical interpretation as a representation of the strongly chirped pulses in mode-locked both solid-state and fiber oscillators. Scaling properties of such pulses demonstrate a feasibility of sub-mJ pulse generation in the continuous-wave mode-locking regime directly from an oscillator operating at the MHz repetition rate.

  13. Topics in soliton theory

    CERN Document Server

    Carroll, RW

    1991-01-01

    When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and K

  14. Solitons on Singularities

    CERN Document Server

    Halyo, Edi

    2009-01-01

    We describe solitons that live on the world--volumes of D5 branes wrapped on deformed $A_2$ singularities fibered over $C(x)$. We show that monopoles are D3 branes wrapped on a node of the deformed singularity and stretched along $C(x)$. F and D--term strings are D3 branes wrapped on a node of a singularity that is deformed and resolved respectively. Domain walls require deformed $A_3$ singularities and correspond to D5 branes wrapped on a node and stretched along $C(x)$.

  15. Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas

    CERN Document Server

    Verheest, Frank; Hereman, Willy A

    2016-01-01

    The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg-de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obta...

  16. Deceleration of the small solitons in the soliton lattice: KdV-type framework

    Science.gov (United States)

    Shurgalina, Ekaterina; Gorshkov, Konstantin; Talipova, Tatiana; Pelinovsky, Efim

    2016-04-01

    As it is known the solitary waves (solitons) in the KdV-systems move with speed which exceeds the speed of propagation of long linear waves (sound speed). Due to interaction between them, solitons do not lose their individuality (elastic interaction). Binary interaction of neigborough solitons is the major contribution in the dynamics of soliton gas. Taking into account the integrability of the classic and modified Korteweg-de Vries equations the process of the soliton interaction can be analyzed in the framework of the rigorous analytical two-soliton solutions. Main physical conclusion from this solution is the phase shift which is positive for large solitons and negative for small solitons. This fact influences the average velocity of individual soliton in the soliton lattice or soliton gas. We demonstrate that soliton of relative small amplitude moves in soliton gas in average in opposite (negative) direction, meanwhile a free soliton moves always in the right direction. Approximated analytical theory is created for the soliton motion in the periodic lattice of big solitons of the same amplitudes, and the critical amplitude of the small soliton changed its averaged speed is found. Numerical simulation is conducted for a statistical assembly of solitons with random amplitudes and phases. The application of developed theory to the long surface and internal waves is discussed.

  17. Observation of dust acoustic multi-solitons in a strongly coupled dusty plasma

    Science.gov (United States)

    Boruah, A.; Sharma, S. K.; Nakamura, Y.; Bailung, H.

    2016-09-01

    The excitation and propagation of low frequency dust acoustic multi-solitons are investigated in an unmagnetized strongly coupled dusty plasma. A floating 2D dusty medium is produced in an RF discharge Ar plasma with silica micro-particles. Dust acoustic perturbations are excited by applying a negative sinusoidal pulse of frequency 1-2 Hz and amplitude 4-20 V to an exciter grid. An initial large amplitude dust density compression breaks into a number of solitary pulses which are identified as dust acoustic solitons. The observed multi-soliton evolution is compared with numerical simulations of modified Korteweg de Vries (KdV)-Burger equation. The characteristics of the generated solitons are in good agreement with the theory.

  18. Basic methods of soliton theory

    CERN Document Server

    Cherednik, I

    1996-01-01

    In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local cons

  19. Multi-wavelength and multi-colour temporal and spatial optical solitons

    DEFF Research Database (Denmark)

    Kivshar, Y. S.; Sukhorukov, A. A.; Ostrovskaya, E. A.;

    2000-01-01

    We present an overview of several novel types of multi- component envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, mult......-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons in Fibonacci optical superlattices....

  20. SMOOTHING BY CONVEX QUADRATIC PROGRAMMING

    Institute of Scientific and Technical Information of China (English)

    Bing-sheng He; Yu-mei Wang

    2005-01-01

    In this paper, we study the relaxed smoothing problems with general closed convex constraints. It is pointed out that such problems can be converted to a convex quadratic minimization problem for which there are good programs in software libraries.

  1. Quantum quadratic operators and processes

    CERN Document Server

    Mukhamedov, Farrukh

    2015-01-01

    Covering both classical and quantum approaches, this unique and self-contained book presents the most recent developments in the theory of quadratic stochastic operators and their Markov and related processes. The asymptotic behavior of dynamical systems generated by classical and quantum quadratic operators is investigated and various properties of quantum quadratic operators are studied, providing an insight into the construction of quantum channels. This book is suitable as a textbook for an advanced undergraduate/graduate level course or summer school in quantum dynamical systems. It can also be used as a reference book by researchers looking for interesting  problems to work on, or useful techniques and discussions of particular problems. Since it includes the latest developments in the fields of quadratic dynamical systems, Markov processes and quantum stochastic processes, researchers at all levels are likely to find the book inspiring and useful.

  2. Quadratic Tangles in Planar Algebras

    CERN Document Server

    Jones, Vaughan F R

    2010-01-01

    In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.

  3. Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling

    CERN Document Server

    Carbone, Francesco; El, Gennady

    2015-01-01

    We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use the KdV soliton gas as a simplest analytically accessible model yielding major insight into the general properties of soliton gases in integrable systems. Two model problems are considered: (i) the propagation of a `trial' soliton through a one-component `cold' soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and (ii) collision of two cold soliton gases of different amplitudes (soliton gas shock tube problem) leading to the formation of an incoherend dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm relevance of the kinetic equation for solitons as a quantitatively accurate model for macrosco...

  4. Soliton solutions for Davydov solitons in α-helix proteins

    Science.gov (United States)

    Taghizadeh, N.; Zhou, Qin; Ekici, M.; Mirzazadeh, M.

    2017-02-01

    The propagation equation for describing Davydov solitons in α-helix proteins has been investigated analytically. There are seven integration tools to extract analytical soliton solutions. They are the Ricatti equation expansion approach, ansatz scheme, improved extended tanh-equation method, the extend exp(-Ψ(τ)) -expansion method, the extended Jacobi elliptic function expansion method, the extended trial equation method and the extended G ' / G - expansion method.

  5. Quasistable two-dimensional solitons with hidden and explicit vorticity in a medium with competing nonlinearities.

    Science.gov (United States)

    Leblond, Hervé; Malomed, Boris A; Mihalache, Dumitru

    2005-03-01

    We consider basic types of two-dimensional (2D) vortex solitons in a three-wave model combining quadratic chi((2)) and self-defocusing cubic chi((3))(-) nonlinearities. The system involves two fundamental-frequency (FF) waves with orthogonal polarizations and a single second-harmonic (SH) one. The model makes it possible to introduce a 2D soliton, with hidden vorticity (HV). Its vorticities in the two FF components are S(1,2) = +/-1 , whereas the SH carries no vorticity, S(3) = 0 . We also consider an ordinary compound vortex, with 2S(1) = 2S(2) = S(3) = 2 . Without the chi((3))(-) terms, the HV soliton and the ordinary vortex are moderately unstable. Within the propagation distance z approximately 15 diffraction lengths, Z(diffr), the former one turns itself into a usual zero-vorticity (ZV) soliton, while the latter splits into three ZV solitons (the splinters form a necklace pattern, with its own intrinsic dynamics). To gain analytical insight into the azimuthal instability of the HV solitons, we also consider its one-dimensional counterpart, viz., the modulational instability (MI) of a one-dimensional CW (continuous-wave) state with "hidden momentum," i.e., opposite wave numbers in its two components, concluding that such wave numbers may partly suppress the MI. As concerns analytical results, we also find exact solutions for spreading localized vortices in the 2D linear model; in terms of quantum mechanics, these are coherent states with angular momentum (we need these solutions to accurately define the diffraction length of the true solitons). The addition of the chi((3))(-) interaction strongly stabilizes both the HV solitons and the ordinary vortices, helping them to persist over z up to 50 Z(diffr). In terms of the possible experiment, they are completely stable objects. After very long propagation, the HV soliton splits into two ZV solitons, while the vortex with S(3) = 2S(1,2) = 2 splits into a set of three or four ZV solitons.

  6. Thermodynamic volume of cosmological solitons

    Science.gov (United States)

    Mbarek, Saoussen; Mann, Robert B.

    2017-02-01

    We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter a, though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass Mout satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring Mout to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive.

  7. Generalized sine-Gordon solitons

    Energy Technology Data Exchange (ETDEWEB)

    Santos, C dos [Centro de Fisica e Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, 4169-007 Porto (Portugal); Rubiera-Garcia, D, E-mail: cssilva@fc.up.pt, E-mail: rubieradiego@gmail.com [Departamento de Fisica, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)

    2011-10-21

    In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)

  8. Thermodynamic Volume of Cosmological Solitons

    CERN Document Server

    Mbarek, Saoussen

    2016-01-01

    We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter $a$, though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass $M_{out}$ satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring $M_{out}$ to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive.

  9. Soliton structure dynamics in inhomogeneous media

    CERN Document Server

    Guerrero, L E; González, J A

    1998-01-01

    We show that soliton interaction with finite-width inhomogeneities can activate a great number of soliton internal modes. We obtain the exact stationary soliton solution in the presence of inhomogeneities and solve exactly the stability problem. We present a Karhunen-Loeve analysis of the soliton structure dynamics as a time-dependent force pumps energy into the traslational mode of the kink. We show the importance of the internal modes of the soliton as they can generate shape chaos for the soliton as well as cases in which the first shape mode leads the dynamics.

  10. Soliton interactions of integrable models

    Energy Technology Data Exchange (ETDEWEB)

    Ruan Hangyu E-mail: hyruan@mail.nbip.net; Chen Yixin

    2003-08-01

    The solution of integrable (n+1)-dimensional KdV system in bilinear form yields a dromion solution that is localized in all directions. The interactions between two dromions are studied both in analytical and in numerical for three (n+1)-dimensional KdV-type equations (n=1, 2, 3). The same interactive properties between two dromions (solitons) are revealed for these models. The interactions between two dromions (solitons) may be elastic or inelastic for different form of solutions.

  11. Soliton interactions of integrable models

    CERN Document Server

    Ruan Hang Yu

    2003-01-01

    The solution of integrable (n+1)-dimensional KdV system in bilinear form yields a dromion solution that is localized in all directions. The interactions between two dromions are studied both in analytical and in numerical for three (n+1)-dimensional KdV-type equations (n=1, 2, 3). The same interactive properties between two dromions (solitons) are revealed for these models. The interactions between two dromions (solitons) may be elastic or inelastic for different form of solutions.

  12. Highly coherent mid-IR supercontinuum by self-defocusing solitons in lithium niobate waveguides with all-normal dispersion

    DEFF Research Database (Denmark)

    Guo, Hairun; Zhou, Binbin; Zeng, Xianglong;

    2014-01-01

    where no linear dispersion (i.e. non-solitonic) regimes exist within the guiding band. Soliton compressions at 2 mm and 3 mm are investigated, with nano-joule single cycle pulse formations and highly coherent octave-spanning supercontinuum generations. With an alternative design on the waveguide...... dispersion, the soliton spectral tunneling effect is also investigated, with which few-cycle pico-joule pulses at 2 mm are formed by a near-IR pump. © 2014 Optical Society of America....

  13. Kink solitons in DNA

    CERN Document Server

    Zdravković, S; Daniel, M

    2012-01-01

    We here examine the nonlinear dynamics of artificial homogeneous DNA chain relying on the plain-base rotator model. It is shown that such dynamics can exhibit kink and antikink solitons of sine-Gordon type. In that respect we propose possible experimental assays based on single molecule micromanipulation techniques. The aim of these experiments is to excite the rotational waves and to determine their speeds along excited DNA. We propose that these experiments should be conducted either for the case of double stranded (DS) or single stranded (SS) DNA. A key question is to compare the corresponding velocities of the rotational waves indicating which one is bigger. The ratio of these velocities appears to be related with the sign of the model parameter representing ratio of the hydrogen-bonding and the covalent-bonding interaction within the considered DNA chain.

  14. Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type.

    Science.gov (United States)

    Mayteevarunyoo, Thawatchai; Malomed, Boris A; Roeksabutr, Athikom

    2011-08-29

    Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP's duty cycle (DC, i.e., the ratio of the void's width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.

  15. On the structure of gradient Yamabe solitons

    CERN Document Server

    Cao, Huai-Dong; Zhang, Yingying

    2011-01-01

    We show that every complete nontrivial gradient Yamabe soliton admits a special global warped product structure with a one-dimensional base. Based on this, we prove a general classification theorem for complete nontrivial locally conformally flat gradient Yamabe solitons.

  16. Waveguides induced by grey screening solitons

    Institute of Scientific and Technical Information of China (English)

    Lu Ke-Qing; Zhao Wei; Yang Yan-Long; Zhang Mei-Zhi; Li Jin-Ping; Liu Hong-Jun; Zhang Yan-Peng

    2006-01-01

    We investigate the properties of waveguides induced by one-dimensional grey screening solitons in biased photore-fractive crystals. The results show that waveguides induced by grey screening solitons are always of single mode for all intensity ratios, i.e. the ratios between the peak intensity of the soliton and the dark irradiance. Our analysis indicates that the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton increase monotonically with intensity ratio increasing. On the other hand, when the soliton greyness increases, the energy confined near the centre of the grey soliton and the propagation constant of the guided mode of the waveguide induced by the grey screening soliton decrease monotonically. Relevant examples are provided where photorefractive crystal is of the strontium barium niobate type.

  17. Geometric solitons of Hamiltonian flows on manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-12-15

    It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.

  18. Numerical Calculation of a Standing Soliton

    Institute of Scientific and Technical Information of China (English)

    XianchuZHOU; YiRUI

    1999-01-01

    The governing equation of a standing soliton i.e. a cubic Schroedinger equation with a complex conjugate term was simulated in this article.The simulation showed that the linear damping α affects strongly on the formation of a stable standing soliton.Laedke and Spatschek stable condition is a necessary condition,not a sufficient condition.Arbitrary initial disturbance may develop into standing soliton.The interaction of two standing solitons can be simulated.

  19. Analytical theory of dark nonlocal solitons

    DEFF Research Database (Denmark)

    Kong, Qian; Wang, Qi; Bang, Ole;

    2010-01-01

    We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.......We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....

  20. Properties of an optical soliton gas

    Science.gov (United States)

    Schwache, A.; Mitschke, F.

    1997-06-01

    We consider light pulses propagating in an optical fiber ring resonator with anomalous dispersion. New pulses are fed into the resonator in synchronism with its round-trip time. We show that solitary pulse shaping leads to a formation of an ensemble of subpulses that are identified as solitons. All solitons in the ensemble are in perpetual relative motion like molecules in a fluid; thus we refer to the ensemble as a soliton gas. Properties of this soliton gas are determined numerically.

  1. Collapse of Langmuir solitons in inhomogeneous plasmas

    CERN Document Server

    Chen, Y A; Nishida, Y; Cheng, C Z

    2016-01-01

    Propagation of Langmuir solitons in inhomogeneous plasmas is investigated numerically. Through numerical simulation solving Zakharov equations, the solitons are accelerated toward the low density side. As a consequence, isolated cavities moving at ion sound velocities are emitted. When the acceleration is further increased, solitons collapse and the cavities separate into two lumps released at ion sound velocities. The threshold is estimated by an analogy between the soliton and a particle overcoming the self-generated potential well.

  2. Students' understanding of quadratic equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  3. Finite dimensional quadratic Lie superalgebras

    CERN Document Server

    Jarvis, Peter; Yates, Luke

    2010-01-01

    We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.

  4. Integrable vs Nonintegrable Geodesic Soliton Behavior

    CERN Document Server

    Fringer, O B

    1999-01-01

    We study confined solutions of certain evolutionary partial differential equations (pde) in 1+1 space-time. The pde we study are Lie-Poisson Hamiltonian systems for quadratic Hamiltonians defined on the dual of the Lie algebra of vector fields on the real line. These systems are also Euler-Poincare equations for geodesic motion on the diffeomorphism group in the sense of the Arnold program for ideal fluids, but where the kinetic energy metric is different from the L2 norm of the velocity. These pde possess a finite-dimensional invariant manifold of particle-like (measure-valued) solutions we call ``pulsons.'' We solve the particle dynamics of the two-pulson interaction analytically as a canonical Hamiltonian system for geodesic motion with two degrees of freedom and a conserved momentum. The result of this two-pulson interaction for rear-end collisions is elastic scattering with a phase shift, as occurs with solitons. In contrast, head-on antisymmetric collisons of pulsons tend to form singularities.

  5. Successive quadratic programming multiuser detector

    Institute of Scientific and Technical Information of China (English)

    Mu Xuewen; Zhang Yaling; Liu Sanyang

    2007-01-01

    Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem,a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

  6. Integer Quadratic Quasi-polyhedra

    Science.gov (United States)

    Letchford, Adam N.

    This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.

  7. Soliton resonance in bose-einstein condensate

    Science.gov (United States)

    Zak, Michail; Kulikov, I.

    2002-01-01

    A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

  8. Control of optical solitons by light waves.

    Science.gov (United States)

    Grigoryan, V S; Hasegawa, A; Maruta, A

    1995-04-15

    A new method of controlling optical solitons by means of light wave(s) in fibers is presented. By a proper choice of light wave(s), parametric four-wave mixing can control the soliton shape as well as the soliton parameters (amplitude, frequency, velocity, and position).

  9. THE PHYSICAL MECHANISM OF COLLISION BETWEEN SOLITONS

    Institute of Scientific and Technical Information of China (English)

    张卓; 唐翌; 颜晓红

    2001-01-01

    An easy and general way to access more complex soliton phenomena is introduced in this paper. The collisionprocess between two solitons of the KdV equation is investigated in great detail with this novel approach, which is different from the sophisticated method of inverse scattering transformation. A more physical and transparent picture describing the collision of solitons is presented.

  10. Soliton bunching in annular Josephson junctions

    DEFF Research Database (Denmark)

    Vernik, I.V; Lazarides, Nickos; Sørensen, Mads Peter

    1996-01-01

    By studying soliton (fluxon) motion in long annular Josephson junctions it is possible to avoid the influence of the boundaries and soliton-soliton collisions present in linear junctions. A new experimental design consisting of a niobium coil placed on top of an annular junction has been used...

  11. Soliton modulation instability in fiber lasers

    Science.gov (United States)

    Tang, D. Y.; Zhao, L. M.; Wu, X.; Zhang, H.

    2009-08-01

    We report experimental evidence of soliton modulation instability in erbium-doped fiber lasers. An alternate type of spectral sideband generation was always experimentally observed on the soliton spectrum of the erbium-doped soliton fiber lasers when energy of the formed solitons reached beyond a certain threshold value. Following this spectral sideband generation, if the pump power of the lasers was further increased, either a new soliton would be formed or the existing solitons would experience dynamical instabilities, such as the period-doubling bifurcations or period-doubling route to chaos. We point out that the mechanism for this soliton spectral sideband generation is the modulation instability of the solitons in the lasers. We further show that, owing to the internal energy balance of a dissipative soliton, modulation instability itself does not destroy the stable soliton evolution in a laser cavity. It is the strong resonant wave coupling between the soliton and dispersive waves that leads to the dynamic instability of the solitons.

  12. Attraction of nonlocal dark optical solitons

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov; Neshev, Dragomir; Krolikowski, Wieslaw

    2004-01-01

    We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states...... of dark solitons. (C) 2004 Optical Society of America...

  13. Incoherently Coupled Grey Photovoltaic Spatial Soliton Families

    Institute of Scientific and Technical Information of China (English)

    WANG Hong-Cheng; SHE Wei-Long

    2005-01-01

    @@ A theory is developed for incoherently coupled grey photovoltaic soliton families in unbiased photovoltaic crystals.Both the properties and the forming conditions of these soliton families are discussed in detail The theory canalso be used to investigate the dark photovoltaic soliton families. Some relevant examples are presented, in which the photovoltaic-photorefractive crystal is of lithium niobate type.

  14. Ultra-short laser pulse compression by using the group-velocity-matched cascaded quadratic nonlinearity∗%利用群速度匹配的级联二阶非线性实现超短激光脉冲压缩*

    Institute of Scientific and Technical Information of China (English)

    叶荣; 张彬; 李恪宇

    2013-01-01

      提出了一种采用倾斜脉冲的级联二阶非线性来实现超短激光脉冲压缩的方法.对基于单块BBO晶体中基频光与倍频光群速度匹配的级联二阶非线性的脉冲压缩方案进行了理论分析.对比研究了群速度匹配与失配情况下利用级联二阶非线性进行脉冲压缩的效果,并模拟分析了基频光与倍频光的位相失配量、非线性晶体长度、基频光初始峰值光强和初始脉宽等因素对脉冲压缩效果的影响.结果表明,基频光与倍频光的群速度匹配将会大幅度改善压缩脉冲的时间波形和频谱分布.通过对位相失配量、晶体长度、初始光强等参数的优化和选取可获得较理想的压缩效果.采用倾斜脉冲的级联二阶非线性的脉宽压缩方法,针对中心波长800 nm、脉宽100 fs,峰值光强为50 GW/cm2的基频光脉冲,采用25 mm厚BBO晶体,当基频光与倍频光位相失配量∆k=60 mm−1(对应失谐角1.98◦),晶体外部脉冲前沿倾斜角γ0=74◦时,计算获得了质量较好的20 fs剩余基频光,并同时产生了14 fs的倍频光.%A new method for compressing ultra-short laser pulse has been proposed in which cascaded quadratic nonlinearity with tilt pulse is used. The pulse compression scheme with group velocity matching between fundamental harmonic (FH) and second harmonic (SH) pulses in a single BBO crystal has been analyzed theoretically. The compressed results have been investigated and compared between the cases of group velocity matching and mismatching. Furthermore, the influences of the phase mismatching between the FH and SH pulses, the length of the nonlinear crystal, the initial peak intensity and pulse-duration of the FH pulse on the pulse-duration compression have been analyzed and simulated. The results show that the matched group velocity between FH and SH pulses can improve significantly both the temporal profile and the spectrum distribution of the compressed pulse. High

  15. Dynamics of the Davydov–Scott soliton with location or velocity mismatch of its high-frequency component

    Energy Technology Data Exchange (ETDEWEB)

    Blyakhman, L.G.; Gromov, E.M.; Onosova, I.V.; Tyutin, V.V., E-mail: vtyutin@hse.ru

    2017-05-03

    The dynamics of a two-component Davydov–Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg–de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton's component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations. - Highlights: • The dynamics of the Davydov–Scott soliton with initial location or velocity mismatch of the HF component was investigated. • The study was performed within the framework of coupled linear Schrödinger and KdV equations for the HF and LF fields. • Analytical and numerical approaches were used. • The frequency of the DS soliton component oscillation was found. • Stability of the perturbed DS solitons was demonstrated.

  16. Complex solitons with real energies

    Science.gov (United States)

    Cen, Julia; Fring, Andreas

    2016-09-01

    Using Hirota’s direct method and Bäcklund transformations we construct explicit complex one and two-soliton solutions to the complex Korteweg-de Vries (KdV) equation, the complex modified KdV (mKdV) equation and the complex sine-Gordon equation. The one-soliton solutions of trigonometric and elliptic type turn out to be { P }{ T }-symmetric when a constant of integration is chosen to be purely imaginary with one special choice corresponding to solutions recently found by Khare and Saxena. We show that alternatively complex { P }{ T }-symmetric solutions to the KdV equation may also be constructed alternatively from real solutions to the mKdV by means of Miura transformations. The multi-soliton solutions obtained from Hirota’s method break the { P }{ T }-symmetric, whereas those obtained from Bäcklund transformations are { P }{ T }-invariant under certain conditions. Despite the fact that some of the Hamiltonian densities are non-Hermitian, the total energy is found to be positive in all cases, that is irrespective of whether they are { P }{ T }-symmetric or not. The reason is that the symmetry can be restored by suitable shifts in space-time and the fact that any of our N-soliton solutions may be decomposed into N separate { P }{ T }-symmetrizable one-soliton solutions.

  17. Unramified extensions of quadratic fields

    Institute of Scientific and Technical Information of China (English)

    Wei Li; Dong Yang; Xianke Zhang

    2008-01-01

    Let K be a global quadratic field, then every unramified abelian extension of K is proved to be absolutely Galois when K is a number field or under some natural conditions when K is a function field. The absolute Galois group is also determined explicitly.

  18. Quadratic prediction of factor scores

    NARCIS (Netherlands)

    Wansbeek, T

    1999-01-01

    Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

  19. Quadratic Variation by Markov Chains

    DEFF Research Database (Denmark)

    Hansen, Peter Reinhard; Horel, Guillaume

    We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...

  20. Dynamics of Soliton Cascades in Fiber Amplifiers

    CERN Document Server

    Arteaga-Sierra, F R; Agrawal, Govind P

    2016-01-01

    We study numerically the formation of cascading solitons when femtosecond optical pulses are launched into a fiber amplifier with less energy than required to form a soliton of equal duration. As the pulse is amplified, cascaded fundamental solitons are created at different distances, without soliton fission, as each fundamental soliton moves outside the gain bandwidth through the Raman-induced spectral shifts. As a result, each input pulse creates multiple, temporally separated, ultrashort pulses of different wavelengths at the amplifier output. The number of pulses depends not only on the total gain of the amplifier but also on the width of input pulses.

  1. Quark structure of chiral solitons

    CERN Document Server

    Diakonov, D

    2004-01-01

    There is a prejudice that the chiral soliton model of baryons is something orthogonal to the good old constituent quark models. In fact, it is the opposite: the spontaneous chiral symmetry breaking in strong interactions explains the appearance of massive constituent quarks of small size thus justifying the constituent quark models, in the first place. Chiral symmetry ensures that constituent quarks interact very strongly with the pseudoscalar fields. The ``chiral soliton'' is another word for the chiral field binding constituent quarks. We show how the old SU(6) quark wave functions follow from the ``soliton'', however, with computable relativistic corrections and additional quark-antiquark pairs. We also find the 5-quark wave function of the exotic baryon Theta+.

  2. Surface solitons in trilete lattices

    CERN Document Server

    Stojanovic, M; Hadzievski, Lj; Malomed, B A

    2011-01-01

    Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schr\\"{o}dinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter -- actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, ...

  3. Topological Solitons and Folded Proteins

    CERN Document Server

    Chernodub, M N; Niemi, Antti J

    2010-01-01

    We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 0.7 Angstrom or less for the central alpha-carbons, i.e. within the limits of current experimental accuracy.

  4. Solitons in Bose–Einstein condensates

    Indian Academy of Sciences (India)

    Radha Balakrishnan; Indubala I Satija

    2011-11-01

    The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.

  5. Regularized degenerate multi-solitons

    CERN Document Server

    Correa, Francisco

    2016-01-01

    We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schroedinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Baecklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.

  6. The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions

    CERN Document Server

    Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert

    2010-01-01

    We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.

  7. Consensus-ADMM for General Quadratically Constrained Quadratic Programming

    Science.gov (United States)

    Huang, Kejun; Sidiropoulos, Nicholas D.

    2016-10-01

    Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for general QCQP. The problem is first reformulated in consensus optimization form, to which the alternating direction method of multipliers (ADMM) can be applied. The reformulation is done in such a way that each of the sub-problems is a QCQP with only one constraint (QCQP-1), which is efficiently solvable irrespective of (non-)convexity. The core components are carefully designed to make the overall algorithm more scalable, including efficient methods for solving QCQP-1, memory efficient implementation, parallel/distributed implementation, and smart initialization. The proposed algorithm is then tested in two applications: multicast beamforming and phase retrieval. The results indicate superior performance over prior state-of-the-art methods.

  8. Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups

    CERN Document Server

    Batat, Wafaa

    2011-01-01

    We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.

  9. Breaking soliton equations and negative-order breaking soliton equations of typical and higher orders

    Indian Academy of Sciences (India)

    ABDUL-MAJID WAZWAZ

    2016-11-01

    We develop breaking soliton equations and negative-order breaking soliton equations of typical and higher orders. The recursion operator of the KdV equation is used to derive these models.We establish the distinctdispersion relation for each equation. We use the simplified Hirota’s method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop generalized dispersion relations for the typical breaking soliton equations and the generalized negative-order breaking soliton equations. The results provide useful information on the dynamics of the relevant nonlinear negative-order equations.

  10. Dark and bright solitons for a three-dimensional Gross-Pitaevskii equation with distributed time-dependent coefficients in the Bose-Einstein condensation

    Science.gov (United States)

    Liu, Lei; Tian, Bo; Zhen, Hui-Ling; Wu, Xiao-Yu; Shan, Wen-Rui

    2017-02-01

    Under investigation in this paper is a three-dimensional Gross-Pitaevskii equation with the distributed time-dependent coefficients, which describes the phenomena associated with the three-dimensional Bose-Einstein condensation. Under the constraint α(t) = 2 β(t) , we obtain the bilinear forms, dark and bright N-soliton solutions via the Hirota method and symbolic computation, where t is the scaled time, α(t) and β(t) are the coefficients for the strength of the quadratic potential and diffraction, respectively. Specially, compared with the bright soliton solutions previously reported, we eliminate one constraint and obtain more soliton parameters. We give the existence constraints of the dark and bright N solitons, respectively. Choosing the diffraction and gain/loss coefficients, we observe the growth, decay, periodic oscillation, periodic collapse and revival of the dark and bright solitons. Relationships between the BEC time-dependent coefficients and soliton properties are studied. With the help of the asymptotic and graphic analysis, elastic interactions of the dark and bright two solitons are exhibited.

  11. Quadratic and 2-Crossed Modules of Algebras

    Institute of Scientific and Technical Information of China (English)

    Z. Arvasi; E. Ulualan

    2007-01-01

    In this work, we define the quadratic modules for commutative algebras and give relations among 2-crossed modules, crossed squares, quadratic modules and simplicial commutative algebras with Moore complex of length 2.

  12. New Soliton-like Solutions and Multi-soliton Structures for Broer-Kaup System with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    By using the further extended tanh method [Phys. Lett. A 307 (2003) 269; Chaos, Solitons & Fractals 17(2003) 669] to the Broer-Kaup system with variable coefficients, abundant new soliton-like solutions and multi-soliton-like solutions are derived. Based on the derived multi-soliton-like solutions which contain arbitrary functions, some interesting multi-soliton structures are revealed.

  13. Soliton solutions and gauge equivalence for the problem of Zakharov-Shabat and its generalizations

    Science.gov (United States)

    Vaklev, Y.

    1996-03-01

    In a paper by Takhtadjan and Faddeev [Hamiltonian approach to the soliton theory (in Russian) (Nauka, Moskov, 1986)] the N-soliton solutions, related to the nonlinear Schrödinger equation (NSE), are given. A generalization of this approach allows us to apply it not only to the NSE, but to the whole hierarchy of the Zakharov-Shabat problem, to the quadratic bundle problem, and to the ones gauge equivalent to them [where one can find, for example, the Heisenberg ferromagnet equation, the relativistic Mikhailov model (which, in appropriate reduction, is equivalent to the massive Thirring model), the derivative nonlinear Schrödinger equation (which is equivalent to the derivative Landau-Lifshitz equation), etc.]. We have used an appropriate reduction, giving us interesting, from a physical point of view, results. Thus we manage to obtain the soliton solutions for the whole hierarchy of the quadratic bundle problem (free and under reduction) and for the ones gauge equivalent to it. This result was first announced in previous articles by Vaklev, but here we manage to solve the determinants given there and to present the searched result as simple fractions of products of numerical differences.

  14. Team Decision Problems with Convex Quadratic Constraints

    OpenAIRE

    Gattami, Ather

    2015-01-01

    In this paper, we consider linear quadratic team problems with an arbitrary number of quadratic constraints in both stochastic and deterministic settings. The team consists of players with different measurements about the state of nature. The objective of the team is to minimize a quadratic cost subject to additional finite number of quadratic constraints. We first consider the problem of countably infinite number of players in the team for a bounded state of nature with a Gaussian distributi...

  15. Chiral asymmetry in propagation of soliton defects in crystalline backgrounds

    CERN Document Server

    Arancibia, Adrian

    2015-01-01

    By applying Darboux-Crum transformations to the Lax pair formulation of the Korteweg-de Vries (KdV) equation, we construct new sets of multi-soliton solutions to it as well as to the modified Korteweg-de Vries (mKdV) equation. The obtained solutions exhibit a chiral asymmetry in propagation of different types defects in crystalline backgrounds. We show that the KdV solitons of pulse and compression modulation types, which support bound states in semi-infinite and finite forbidden bands in the spectrum of the perturbed quantum one-gap Lame system, propagate in opposite directions with respect to the asymptotically periodic background. A similar but more complicated picture also appears for the multi-kink-antikink mKdV solitons that propagate with a privileged direction over topologically trivial or topologically nontrivial crystalline background in dependence on position of energy levels of the trapped bound states in spectral gaps of the associated Dirac system. Exotic N=4 nonlinear supersymmetric structure i...

  16. PIC simulation of compressive and rarefactive dust ion-acoustic solitary waves

    Science.gov (United States)

    Li, Zhong-Zheng; Zhang, Heng; Hong, Xue-Ren; Gao, Dong-Ning; Zhang, Jie; Duan, Wen-Shan; Yang, Lei

    2016-08-01

    The nonlinear propagations of dust ion-acoustic solitary waves in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated by the particle-in-cell method. By comparing the simulation results with those obtained from the traditional reductive perturbation method, it is observed that the rarefactive KdV solitons propagate stably at a low amplitude, and when the amplitude is increased, the prime wave form evolves and then gradually breaks into several small amplitude solitary waves near the tail of soliton structure. The compressive KdV solitons propagate unstably and oscillation arises near the tail of soliton structure. The finite amplitude rarefactive and compressive Gardner solitons seem to propagate stably.

  17. A polyhedral approach to quadratic assignment problem

    OpenAIRE

    Köksaldı, Ahmet Sertaç Murat

    1994-01-01

    Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1994. Thesis (Master's) -- Bilkent University, 1994. Includes bibliographical references. In this thesis, Quadratic Assignment Problem is considered. Since Quadratic Assignment Problem is JVP-bard, no polynomial time exact solution method exists. Proving optimality of solutions to Quadratic Assignment Problems has been limited to instances of small dimension. In...

  18. Orthogonality preserving infinite dimensional quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Akın, Hasan [Department of Mathematics, Faculty of Education, Zirve University, Gaziantep, 27260 (Turkey); Mukhamedov, Farrukh [Department of Computational & Theoretical Sciences Faculty of Science, International Islamic University Malaysia P.O. Box, 141, 25710, Kuantan Pahang (Malaysia)

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  19. Extending the Scope of Robust Quadratic Optimization

    NARCIS (Netherlands)

    Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

    2017-01-01

    In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in ge

  20. Quantum bouncer with quadratic dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, G. [NanoScience Technology Center, University of Central Florida, Orlando, FL 32826 (United States)]. e-mail: ggonzalez@physics.ucf.edu

    2008-07-01

    The energy loss due to a quadratic velocity-dependent force on a quantum particle bouncing off a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new, effective, phenomenological Hamiltonian which corresponds to the actual energy of the system and obtain the correction to the eigenvalues of the energy in first-order quantum perturbation theory for the case of weak dissipation. (Author)

  1. Quantum bouncer with quadratic dissipation

    Science.gov (United States)

    González, G.

    2008-02-01

    The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.

  2. Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

    Energy Technology Data Exchange (ETDEWEB)

    Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)

    2004-05-01

    We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.

  3. Numerical investigation of acoustic solitons

    CERN Document Server

    Lombard, Bruno; Richoux, Olivier

    2014-01-01

    Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves.

  4. Solitons in a wave tank

    Science.gov (United States)

    Olsen, M.; Smith, H.; Scott, A. C.

    1984-09-01

    A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations.

  5. Subwavelength vortical plasmonic lattice solitons.

    Science.gov (United States)

    Ye, Fangwei; Mihalache, Dumitru; Hu, Bambi; Panoiu, Nicolae C

    2011-04-01

    We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.

  6. Langmuir Solitons in Magnetized Plasmas

    DEFF Research Database (Denmark)

    Dysthe, K. B.; Mjølhus, E.; Pécseli, Hans;

    1978-01-01

    The authors have considered the nonlinear interaction between a high frequency (Langmuir) wave, which propagates at an arbitrary angle to a weak, constant magnetic field, and low frequency (ion-cyclotron or ion-sound) perturbations. In studying Langmuir envelope solitons they have unified...

  7. Solitons in a wave tank

    DEFF Research Database (Denmark)

    Olsen, M.; Smith, H.; Scott, Alwyn C.

    1984-01-01

    A wave tank experiment (first described by the nineteenth-century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment...

  8. Global Optimization of a Class of Nonconvex Quadratically Constrained Quadratic Programming Problems

    Institute of Scientific and Technical Information of China (English)

    Yong XIA

    2011-01-01

    In this paper we study a class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems.We show that each problem is polynomially solved.Strong duality holds if a redundant constraint is introduced.As an application,a new lower bound is proposed for the quadratic assignment problem.

  9. A hybrid soliton-based system: generation and steering of cavity solitons by means of photorefractive soliton electro-activation

    CERN Document Server

    Columbo, Lorenzo; Brambilla, Massimo; Prati, Franco; Tissoni, Giovanna

    2012-01-01

    We propose a hybrid soliton-based system consisting of a centrosymmetric photorefractive crystal, supporting photorefractive solitons, coupled to a vertical cavity surface emitting laser, supporting multistable cavity solitons. The composite nature of the system, which couples a propagative/conservative field dynamics to a stationary/dissipative one, allows to observe a more general and unified system phenomenology and to conceive novel photonic functionalities. The potential of the proposed hybrid system becomes clear when investigating the generation and control of cavity solitons by propagating a plane wave through electro-activated solitonic waveguides in the crystal. By changing the electro-activation voltage of the crystal, we prove that cavity solitons can be turned on and shifted with controlled velocity across the device section. The scheme can be exploited for applications to optical information encoding and processing.

  10. Dissipative Kerr solitons in optical microresonators

    CERN Document Server

    Herr, Tobias; Kippenberg, Tobias J

    2015-01-01

    This chapter describes the discovery and stable generation of temporal dissipative Kerr solitons in continuous-wave (CW) laser driven optical microresonators. The experimental signatures as well as the temporal and spectral characteristics of this class of bright solitons are discussed. Moreover, analytical and numerical descriptions are presented that do not only reproduce qualitative features but can also be used to accurately model and predict the characteristics of experimental systems. Particular emphasis lies on temporal dissipative Kerr solitons with regard to optical frequency comb generation where they are of particular importance. Here, one example is spectral broadening and self-referencing enabled by the ultra-short pulsed nature of the solitons. Another example is dissipative Kerr soliton formation in integrated on-chip microresonators where the emission of a dispersive wave allows for the direct generation of unprecedentedly broadband and coherent soliton spectra with smooth spectral envelope.

  11. Soliton dynamics in the multiphoton plasma regime

    CERN Document Server

    Husko, Chad A; Colman, Pierre; Zheng, Jiangjun; De Rossi, Alfredo; Wong, Chee Wei; 10.1038/srep01100

    2013-01-01

    Solitary waves have consistently captured the imagination of scientists, ranging from fundamental breakthroughs in spectroscopy and metrology enabled by supercontinuum light, to gap solitons for dispersionless slow-light, and discrete spatial solitons in lattices, amongst others. Recent progress in strong-field atomic physics include impressive demonstrations of attosecond pulses and high-harmonic generation via photoionization of free-electrons in gases at extreme intensities of 1014 Wcm2. Here we report the first phase-resolved observations of femtosecond optical solitons in a semiconductor microchip, with multiphoton ionization at picojoule energies and 1010 Wcm2 intensities. The dramatic nonlinearity leads to picojoule observations of free-electron-induced blue-shift at 1016 cm3 carrier densities and self-chirped femtosecond soliton acceleration. Furthermore, we evidence the time-gated dynamics of soliton splitting on-chip, and the suppression of soliton recurrence due to fast free-electron dynamics. Thes...

  12. Vectorial coupled-mode solitons in one-dimensional photonic crystals

    Institute of Scientific and Technical Information of China (English)

    朱善华; 黄国翔; 崔维娜

    2002-01-01

    We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadraticand cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopesof two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification arederived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-modeequations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due tothe optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears whenthe frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.

  13. Solitons at the critical density of negative ions in multicomponent plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Ibohanbi Singh, K.H.; Das, G.C. (Manipur Univ., Dept. of Mathematics, Imphal (IN))

    1989-12-01

    The derivation of solitary waves in generalized multicomponent plasmas shows that the negative ion introduces a critical density at which the characteristics of the solitons are studied. The soliton's behavior deriving through the Korteweg-deVries (K-dV) equation at the critical density shows that the nonlinearity of the wave vanishes, due to which the mode of study is augmented through a modified K-dV equation. Employing a higher order equation involving quadratic and cubic nonlinearities, the transition of the K-dV equation to a modified K-dV equation along with the conservation of the Sagdeev potential, which is not affected by the negative ions, is studied in detail. The results are compared with experimental observations.

  14. Observation of soliton-induced resonant radiation due to three-wave mixing

    CERN Document Server

    Zhou, B; Guo, H R; Zeng, X L; Chen, X F; Chung, H P; Chen, Y H; Bache, M

    2016-01-01

    We show experimental proof that three-wave mixing can lead to formation of resonant radiation when interacting with a temporal soliton. This constitutes a new class of resonant waves, and due to the parametric nature of the three-wave mixing nonlinearity, the resonant radiation frequencies are widely tunable over broad ranges in the visible and mid-IR. The experiment is conducted in a periodically poled lithium niobate crystal, where a femtosecond self-defocusing soliton is excited in the near-IR, and resonant radiation due to the sum- and difference-frequency generation quadratic nonlinear terms are observed in the near- and mid-IR, respectively. Their spectral positions are widely tunable by changing the poling pitch and are in perfect agreement with theoretical calculations.

  15. Wavelength conversion through soliton self-frequency shift in tellurite microstructured fiber with picosecond pump pulse

    Science.gov (United States)

    Bi, Wanjun; Li, Xia; Xing, Zhaojun; Zhou, Qinling; Fang, Yongzheng; Gao, Weiqing; Xiong, Liangming; Hu, Lili; Liao, Meisong

    2016-01-01

    Wavelength conversion to the wavelength range that is not covered by commercially available lasers could be accomplished through the soliton self-frequency shift (SSFS) effect. In this study, the phenomenon of SSFS pumped by a picosecond-order pulse in a tellurite microstructured fiber is investigated both theoretically and experimentally. The balance between the dispersion and the nonlinearity achieved by a 1958 nm pump laser induces a distinct SSFS effect. Attributed to the large spectral distance between the pump pulse and the fiber zero-dispersion wavelength, the SSFS is not cancelled due to energy shedding from the soliton to the dispersive wave. Details about the physical mechanisms behind this phenomenon and the variations of the wavelength shift, the conversion efficiency are revealed based on numerical simulations. Owing to the large soliton number N, the pulse width of the first split fundamental soliton is approximately 40 fs, producing a pulse compression factor of ˜38, much higher than that pumped by a femtosecond pulse. Experiments were also conducted to confirm the validity of the simulation results. By varying the pump power, a continuous soliton shift from 1990 nm to 2264 nm was generated. The generation of SSFS in tellurite microstructured fibers with picosecond pump pulse can provide a new approach for wavelength conversion in the mid-infrared range and could be useful in medical and some other areas.

  16. Solitones embebidos: estables, inestables, continuos y discretos

    OpenAIRE

    J. Fujioka; R. F. Rodríguez; A. Espinosa-Cerón

    2006-01-01

    En 1997 se descubrió un nuevo tipo de solitones, bautizados en 1999 como solitones embebidos . Estas peculiares ondas no lineales son interesantes porque existen bajo condiciones en las que hasta hace poco se creía que la propagación de ondas solitarias era imposible. En este trabajo se explica qué son los solitones embebidos, en qué modelos se han encontrado, y qué variantes existen(estables, inestables, continuos, discretos, etc.).

  17. Dynamics of Incoherent Photovoltaic Spatial Solitons

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yi-Qi; LU Ke-Qing; ZHANG Mei-Zhi; LI Ke-Hao; LIU Shuang; ZHANG Yan-Peng

    2009-01-01

    Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time.Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton,grey-like incoherent photovoltaic soliton,incoherent soliton doublet and triplet can be established under proper conditions,but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.

  18. Asymptotic Normality of Quadratic Estimators.

    Science.gov (United States)

    Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad

    2016-12-01

    We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

  19. quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    A. R. Bahadir

    2002-01-01

    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  20. Optimal control linear quadratic methods

    CERN Document Server

    Anderson, Brian D O

    2007-01-01

    This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

  1. Factorization method of quadratic template

    Science.gov (United States)

    Kotyrba, Martin

    2017-07-01

    Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

  2. Soliton coding for secured optical communication link

    CERN Document Server

    Amiri, Iraj Sadegh; Idrus, Sevia Mahdaliza

    2015-01-01

    Nonlinear behavior of light such as chaos can be observed during propagation of a laser beam inside the microring resonator (MRR) systems. This Brief highlights the design of a system of MRRs to generate a series of logic codes. An optical soliton is used to generate an entangled photon. The ultra-short soliton pulses provide the required communication signals to generate a pair of polarization entangled photons required for quantum keys. In the frequency domain, MRRs can be used to generate optical millimetre-wave solitons with a broadband frequency of 0?100 GHz. The soliton signals are multi

  3. Electrical solitons theory, design, and applications

    CERN Document Server

    Ricketts, David S

    2010-01-01

    The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain.Drawing on the award winning research of Carnegie Mellon's David S. Ricketts, Electrical Solitons Theory, Design, and Applications i

  4. Moving stable solitons in Galileon theory

    Energy Technology Data Exchange (ETDEWEB)

    Masoumi, Ali, E-mail: ali@phys.columbia.edu [Physics Department and ISCAP, Columbia University, New York, NY 10027 (United States); Xiao Xiao, E-mail: xx2146@columbia.edu [Physics Department and ISCAP, Columbia University, New York, NY 10027 (United States)

    2012-08-29

    Despite the no-go theorem Endlich et al. (2011) which rules out static stable solitons in Galileon theory, we propose a family of solitons that evade the theorem by traveling at the speed of light. These domain-wall-like solitons are stable under small fluctuations-analysis of perturbation shows neither ghost-like nor tachyon-like instabilities, and perturbative collision of these solitons suggests that they pass through each other asymptotically, which maybe an indication of the integrability of the theory itself.

  5. Observation of attraction between dark solitons

    DEFF Research Database (Denmark)

    Dreischuh, A.; Neshev, D.N.; Petersen, D.E.

    2006-01-01

    We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as ......We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems...

  6. Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

    Energy Technology Data Exchange (ETDEWEB)

    Pelinovsky, E.N. [Department of Information Systems, National Research University – Higher School of Economics, Nizhny Novgorod (Russian Federation); Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Shurgalina, E.G.; Sergeeva, A.V.; Talipova, T.G. [Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod (Russian Federation); Department of Applied Mathematics, Nizhny Novgorod State Technical University, Nizhny Novgorod (Russian Federation); El, G.A., E-mail: g.el@lboro.ac.uk [Department of Mathematical Sciences, Loughborough University (United Kingdom); Grimshaw, R.H.J. [Department of Mathematical Sciences, Loughborough University (United Kingdom)

    2013-01-03

    Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.

  7. Regularized degenerate multi-solitons

    Science.gov (United States)

    Correa, Francisco; Fring, Andreas

    2016-09-01

    We report complex {P}{T} -symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.

  8. Polarization Properties of Laser Solitons

    Directory of Open Access Journals (Sweden)

    Pedro Rodriguez

    2017-04-01

    Full Text Available The objective of this paper is to summarize the results obtained for the state of polarization in the emission of a vertical-cavity surface-emitting laser with frequency-selective feedback added. We start our research with the single soliton; this situation presents two perpendicular main orientations, connected by a hysteresis loop. In addition, we also find the formation of a ring-shaped intensity distribution, the vortex state, that shows two homogeneous states of polarization with very close values to those found in the soliton. For both cases above, the study shows the spatially resolved value of the orientation angle. It is important to also remark the appearance of a non-negligible amount of circular light that gives vectorial character to all the different emissions investigated.

  9. Stability of the equilibrium positions of an engine with nonlinear quadratic springs

    Science.gov (United States)

    Stănescu, Nicolae-Doru; Popa, Dinel

    2014-06-01

    Our paper realizes a study of the equilibrium positions for an engine supported by four identical nonlinear springs of quadratic characteristic. The systems with quadratic characteristic are generally avoided because they lead to mathematical complications. Our goal is to realize such a study for an engine supported on quadratic springs. For the model purposed, we established the equations of motion and we discussed the possibilities for the equilibrium positions. Because of the quadratic characteristic of the springs and of the approximations made for the small rotations, the equations obtained for the equilibrium lead us to a paradox, which consists in the existence of an open neighborhood in which there exists an infinity of positions of indifferent equilibrium, or a curve where the equilibrium positions are situated. Moreover, the study of the stability shows that the stability is assured for the position at which the springs are not compressed. Finally, a numerical example is presented and completely solved.

  10. Quadratic reactivity fuel cycle model

    Energy Technology Data Exchange (ETDEWEB)

    Lewins, J.D.

    1985-11-01

    For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau/sup 2/ as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau/sup 2/ in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper.

  11. Soliton propagation in relativistic hydrodynamics

    CERN Document Server

    Fogaça, D A; 10.1016/j.nuclphysa.2007.03.104

    2013-01-01

    We study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. In a previous work we have derived a KdV equation from Euler and continuity equations in non-relativistic hydrodynamics. In the present contribution we extend our formalism to relativistic fluids. We present results for a given equation of state, which is based on quantum hadrodynamics (QHD).

  12. Discrete solitons in graphene metamaterials

    OpenAIRE

    Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail

    2014-01-01

    We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...

  13. Discrete solitons in graphene metamaterials

    Science.gov (United States)

    Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.

    2015-01-01

    We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.

  14. A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

    Science.gov (United States)

    Tang, Chun-Ming; Jian, Jin-Bao

    2008-10-01

    Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.

  15. Observation of Dissipative Bright Soliton and Dark Soliton in an All-Normal Dispersion Fiber Laser

    Directory of Open Access Journals (Sweden)

    Chunyang Ma

    2016-01-01

    Full Text Available This paper proposes a novel way for controlling the generation of the dissipative bright soliton and dark soliton operation of lasers. We observe the generation of dissipative bright and dark soliton in an all-normal dispersion fiber laser by employing the nonlinear polarization rotation (NPR technique. Through adjusting the angle of the polarizer and analyzer, the mode-locked and non-mode-locked regions can be obtained in different polarization directions. Numerical simulation shows that, in an appropriate pump power range, the dissipative bright soliton and dark soliton can be generated simultaneously in the mode-locked and non-mode-locked regions, respectively. If the pump power exceeds the top limit of this range, only dissipative soliton will exist, whereas if it is below the lower bound of this range, only dark soliton will exist.

  16. On Algebraic Approach in Quadratic Systems

    Directory of Open Access Journals (Sweden)

    Matej Mencinger

    2011-01-01

    Full Text Available When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (nonchaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960. We resume some connections between the dynamics of the quadratic systems and (algebraic properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.

  17. The Worldvolume Action of Kink Solitons in AdS Spacetime

    CERN Document Server

    Khoury, Justin; Stokes, James

    2012-01-01

    A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS space-time is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in its extrinsic and intrinsic curvatures. Two alternative methods are given for doing this. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk space-time.

  18. Highly coherent mid-IR supercontinuum by self-defocusing solitons in lithium niobate waveguides with all-normal dispersion.

    Science.gov (United States)

    Guo, Hairun; Zhou, Binbin; Zeng, Xianglong; Bache, Morten

    2014-05-19

    We numerically investigate self-defocusing solitons in a lithium niobate (LN) waveguide designed to have a large refractive index (RI) change. The waveguide evokes strong waveguide dispersion and all-normal dispersion is found in the entire guiding band spanning the near-IR and the beginning of the mid-IR. Meanwhile, a self-defocusing nonlinearity is invoked by the cascaded (phase-mismatched) second-harmonic generation under a quasi-phase-matching pitch. Combining this with the all-normal dispersion, mid-IR solitons can form and the waveguide presents the first all-nonlinear and solitonic device where no linear dispersion (i.e. non-solitonic) regimes exist within the guiding band. Soliton compressions at 2 μm and 3 μm are investigated, with nano-joule single cycle pulse formations and highly coherent octave-spanning supercontinuum generations. With an alternative design on the waveguide dispersion, the soliton spectral tunneling effect is also investigated, with which few-cycle pico-joule pulses at 2 μm are formed by a near-IR pump.

  19. A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation

    Science.gov (United States)

    Chen, Mei-Dan; Li, Xian; Wang, Yao; Li, Biao

    2017-06-01

    With symbolic computation, some lump solutions are presented to a (3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, and 11435005, Ningbo Natural Science Foundation under Grant No. 2015A610159 and the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502 and K.C. Wong Magna Fund in Ningbo University

  20. An Algorithm for Solving Quadratic Programming Problems

    Directory of Open Access Journals (Sweden)

    V. Moraru

    1997-08-01

    Full Text Available Herein is investigated the method of solution of quadratic programming problems. The algorithm is based on the effective selection of constraints. Quadratic programming with constraints-equalities are solved with the help of an algorithm, so that matrix inversion is avoided, because of the more convenient organization of the Calculus. Optimal solution is determined in a finite number of iterations. It is discussed the extension of the algorithm over solving quadratic non-convex programming problems.

  1. Modification of Plasma Solitons by Resonant Particles

    DEFF Research Database (Denmark)

    Karpman, Vladimir; Lynov, Jens-Peter; Michelsen, Poul;

    1979-01-01

    Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide.......Experimental and numerical results are compared with new theoretical results describing soliton propagation and deformation in a strongly magnetized, plasma-loaded waveguide....

  2. Formation of multiple dark photovoltaic spatial solitons

    Indian Academy of Sciences (India)

    Yuhong Zhang; Keqing Lu; Jianbang Guo; Xuewen Long; Xiaohong Hu; Kehao Li

    2012-02-01

    We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark coherent photovoltaic solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, which realizes a progressive transition from a low-order soliton to a sequence of higher-order solitons. The soliton pairs far away from the centre have bigger width and less visibility. In addition, when the distance from the centre of the dark notch increases, the separations between adjacent dark stripes become slightly smaller.

  3. Soliton algebra by vortex-beam splitting.

    Science.gov (United States)

    Minardi, S; Molina-Terriza, G; Di Trapani, P; Torres, J P; Torner, L

    2001-07-01

    We experimentally demonstrate the possibility of breaking up intense vortex light beams into stable and controllable sets of parametric solitons. We report observations performed in seeded second-harmonic generation, but the scheme can be extended to all parametric processes. The number of generated solitons is shown to be determined by a robust arithmetic rule.

  4. Dark Solitons in FPU Lattice Chain

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton.Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.

  5. Temperature effects on the Davydov soliton

    DEFF Research Database (Denmark)

    Cruzeiro, L.; Halding, J.; Christiansen, Peter Leth

    1988-01-01

    As a possible mechanism for energy storage and transport in proteins, Davydov has proposed soliton formation and propagation. In this paper we investigate the stability of Davydov solitons at biological temperatures. From Davydov’s original theory evolution equations are derived quantum mechanica...

  6. Multipole vector solitons in nonlocal nonlinear media.

    Science.gov (United States)

    Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru

    2006-05-15

    We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.

  7. Few-optical-cycle dissipative solitons

    Energy Technology Data Exchange (ETDEWEB)

    Leblond, H [Laboratoire de Photonique d' Angers EA 4464, Universite d' Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01 (France); Mihalache, D, E-mail: herve.leblond@univ-angers.f [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125 (Romania)

    2010-09-17

    By using a powerful reductive perturbation technique, or multiscale analysis, a generalized modified Korteweg-de Vries partial differential equation is derived, which describes the physics of few-optical-cycle dissipative solitons beyond the slowly varying envelope approximation. Numerical simulations of the formation of stable dissipative solitons from arbitrary breather-like few-cycle pulses are also given.

  8. Enhanced pulse compression induced by the interaction between the third-order dispersion and the cross-phase modulation in birefringent fibres

    Institute of Scientific and Technical Information of China (English)

    徐文成; 陈伟成; 张书敏; 罗爱平; 刘颂豪

    2002-01-01

    In this paper, we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres. Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion. while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion.Moreover, there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression.Redshifted initial chirp is helpful to the pulse compression, while blueshifted chirp is detrimental to the pulse compression. There is also an optimal chirp parameter to reach maximum pulse compression. The optimal pulse compression for TOD parameters under different N-order solitons is also found.

  9. The Random Quadratic Assignment Problem

    Science.gov (United States)

    Paul, Gerald; Shao, Jia; Stanley, H. Eugene

    2011-11-01

    The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.

  10. Low-amplitude vector screening solitons

    Institute of Scientific and Technical Information of China (English)

    Keqing Lu(卢克清); Xiangping Zhu(朱香平); Wei Zhao(赵卫); Yanlong Yang(杨延龙); Jinping Li(李金萍); Yanpeng Zhang(张彦鹏); Junchang Zhang(张君昌)

    2004-01-01

    We show self-coupled and cross-coupled vector beam evolution equations in the low-amplitude regime for screening solitons,which can exhibit the analytical solutions of bright-bright and dark-dark vector solitons.Our analysis indicates that these self-coupled vector solitons are obtained irrespective of the intensities of the two optical beams,whereas these cross-coupled vector solitons can be established when the intensities of the two optical beams are equal.Relevant examples are provided where the photorefractive crystal is lithium niobate(LiNbO3).The stability properties of these vector solitons have been investigated numerically and it has been found that they are stable.

  11. Dissipative surface solitons in periodic structures

    CERN Document Server

    Kartashov, Yaroslav V; Vysloukh, Victor A

    2010-01-01

    We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.

  12. Brownian motion of solitons in a Bose-Einstein condensate.

    Science.gov (United States)

    Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B

    2017-03-07

    We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

  13. Binary Quadratic Forms: A Historical View

    Science.gov (United States)

    Khosravani, Azar N.; Beintema, Mark B.

    2006-01-01

    We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

  14. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost type A-source impedance network is proposed in this paper for realizing converters that demand a very high voltage gain. To achieve that, the proposed network uses an auto-transformer, whose obtained gain is quadratically dependent on the duty ratio and is presently not ma...

  15. Quadratic Boost A-Source Impedance Network

    DEFF Research Database (Denmark)

    Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

    2016-01-01

    A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance ...

  16. Factorising a Quadratic Expression with Geometric Insights

    Science.gov (United States)

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  17. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

  18. An example in linear quadratic optimal control

    NARCIS (Netherlands)

    Weiss, George; Zwart, Heiko J.

    1998-01-01

    We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme sim

  19. Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit.

    Science.gov (United States)

    Cai, Xin; Liu, Jinsong; Wang, Shenglie

    2009-02-16

    This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

  20. Soliton dynamics in computational anatomy.

    Science.gov (United States)

    Holm, Darryl D; Ratnanather, J Tilak; Trouvé, Alain; Younes, Laurent

    2004-01-01

    Computational anatomy (CA) has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms. Among these geometric structures, landmarks and image outlines in CA are shown to be singular solutions of a partial differential equation that is called the geodesic EPDiff equation. A recently discovered momentum map for singular solutions of EPDiff yields their canonical Hamiltonian formulation, which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta. The momentum map provides an isomorphism between landmarks (and outlines) for images and singular soliton solutions of the EPDiff equation. This isomorphism suggests a new dynamical paradigm for CA, as well as new data representation.

  1. Edge solitons in the QHE

    CERN Document Server

    Hassaïne, M; Yéra, J C

    2004-01-01

    The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\\"odinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter is an ordinary NLS with time-dependent coefficients which admits interesting solutions. Their arisal is explained by the conformal properties of non-relativistic spacetime. Only the usual travelling soliton is consistent with the jNLS, but the addition of a six-order potential converts it into an integrable equation.

  2. Wave Physics Oscillations - Solitons - Chaos

    CERN Document Server

    Nettel, Stephen

    2009-01-01

    This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.

  3. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  4. Solitons of axion-dilaton gravity

    CERN Document Server

    Bakas, Ioannis

    1996-01-01

    We use soliton techniques of the two-dimensional reduced beta-function equations to obtain non-trivial string backgrounds from flat space. These solutions are characterized by two integers (n, m) referring to the soliton numbers of the metric and axion-dilaton sectors respectively. We show that the Nappi-Witten universe associated with the SL(2) x SU(2) / SO(1, 1) x U(1) CFT coset arises as an (1, 1) soliton in this fashion for certain values of the moduli parameters, while for other values of the soliton moduli we arrive at the SL(2)/SO(1, 1) x SO(1, 1)^2 background. Ordinary 4-dim black-holes arise as 2-dim (2, 0) solitons, while the Euclidean worm-hole background is described as a (0, 2) soliton on flat space. The soliton transformations correspond to specific elements of the string Geroch group. These could be used as starting point for exploring the role of U-dualities in string compactifications to two dimensions.

  5. The Geometrodynamics of Sine-Gordon Solitons

    CERN Document Server

    Gegenberg, J

    1998-01-01

    The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, a...

  6. Quadratic Hedging of Basis Risk

    Directory of Open Access Journals (Sweden)

    Hardy Hulley

    2015-02-01

    Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

  7. On Quadratic Variation of Martingales

    Indian Academy of Sciences (India)

    Rajeeva L Karandikar; B V Rao

    2014-08-01

    We give a construction of an explicit mapping $$\\Psi: D([0,∞),\\mathbb{R})→ D([0,∞),\\mathbb{R}),$$ where $D([0,∞), \\mathbb{R})$ denotes the class of real valued r.c.l.l. functions on $[0,∞)$ such that for a locally square integrable martingale $(M_t)$ with r.c.l.l. paths, $$\\Psi(M.())=A.()$$ gives the quadratic variation process (written usually as $[M,M]_t$) of $(M_t)$. We also show that this process $(A_t)$ is the unique increasing process $(B_t)$ such that $M_t^2-B_t$ is a local martingale, $B_0=0$ and $$\\mathbb{P}(( B)_t=[( M)_t]^2, 0 < ∞)=1.$$ Apart from elementary properties of martingales, the only result used is the Doob’s maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.l.l. martingales.

  8. Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids

    OpenAIRE

    2014-01-01

    Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek $\\Phi$, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton i...

  9. Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids

    OpenAIRE

    Mateo, A. Muñoz; Brand, J.

    2014-01-01

    Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek $\\Phi$, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton i...

  10. R-Hash: Hash Function Using Random Quadratic Polynomials Over GF(2)

    OpenAIRE

    Dhananjoy Dey; Noopur Shrotriya; Indranath Sengupta

    2013-01-01

    In this paper we describe an improved version of HF-hash [7] viz. R-hash: Hash Function Using RandomQuadratic Polynomials Over GF(2). The compression function of HF-hash consists of 32 polynomials with64 variables over GF(2), which were taken from the first 32 polynomials of HFE challenge-1 by forcinglast 16 variables as 0. The mode operation used in computing HF-hash was Merkle-Damgard. We haverandomly selected 32 quadratic non-homogeneous polynomials having 64 variables over GF(2) in case o...

  11. Effect of Soliton Propagation in Fiber Amplifiers

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The propagation of optical solitons in fiber amplifiers is discussed by considering a model that includes linear high order dispersion, two-photon absorption, nonlinear high-order dispersion, self-induced Ramam and five-order nonlinear effects. Based on travelling wave method, the solutions of the nonlinear Schrdinger equations, and the influence on soliton propagation as well as high-order effect in the fiber amplifier are discussed in detail. It is found that because of existing five-order nonlinear effect, the solution is not of secant hyperbola type, but shows high gain state of the fiber amplifier which is very favourable to the propagation of solitons.

  12. Spherical solitons in ion-beam plasma

    Energy Technology Data Exchange (ETDEWEB)

    Das, G.C.; Ibohanbi Singh, K. (Manipur Univ., Imphal (India). Dept. of Mathematics)

    1991-01-01

    By using the reductive perturbation technique, the soliton solution of an ion-acoustic wave radially ingoing in a spherically bounded plasma consisting of ions and ion-beams with multiple electron temperatures is obtained. In sequel to the earlier investigations, the solitary waves are studied as usual through the derivation of a modified Korteweg-de Vries (K-dV) equation in different plasma models arising due to the variation of the isothermality of the plasmas. The characteristics of the solitons are finally compared with those of the planar and the cylindrical solitons. (orig.).

  13. Discrete solitons in coupled active lasing cavities

    CERN Document Server

    Prilepsky, Jaroslaw E; Johansson, Magnus; Derevyanko, Stanislav A

    2012-01-01

    We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active media, where the gain exceeds damping in the linear limit. A zoo of stable localized structures is found and classified: these are bright and grey cavity solitons with different symmetry. It is shown that several new types of solitons with a nontrivial intensity distribution pattern can emerge in the coupled cavities due to the stability of a periodic extended state. The latter can be stable even when a bistability of homogenous states is absent.

  14. Dark solitons in mode-locked lasers

    CERN Document Server

    Ablowitz, Mark J; Nixon, Sean D; Frantzeskakis, Dimitri J

    2010-01-01

    Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model which incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve into dark solitons under appropriate requirements also met in the experimental observations. The resulting pulses are well approximated by dark solitons of the unperturbed nonlinear Schr\\"{o}dinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.

  15. Solitones embebidos: estables, inestables, continuos y discretos

    Directory of Open Access Journals (Sweden)

    J. Fujioka

    2006-01-01

    Full Text Available En 1997 se descubrió un nuevo tipo de solitones, bautizados en 1999 como "solitones embebidos". Estas peculiares ondas no lineales son interesantes porque existen bajo condiciones en las que hasta hace poco se creía que la propagación de ondas solitarias era imposible. En este trabajo se explica qué son los solitones embebidos, en qué modelos se han encontrado, y qué variantes existen(estables, inestables, continuos, discretos, etc..

  16. Stable surface solitons in truncated complex potentials.

    Science.gov (United States)

    He, Yingji; Mihalache, Dumitru; Zhu, Xing; Guo, Lina; Kartashov, Yaroslav V

    2012-07-01

    We show that surface solitons in the one-dimensional nonlinear Schrödinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of the surface solitons shrink with an increase in the amplitude of the imaginary part of complex potential.

  17. Stable surface solitons in truncated complex potentials

    CERN Document Server

    He, Yingji; Zhu, Xing; Guo, Lina; Kartashov, Yaroslav V

    2012-01-01

    We show that surface solitons in the one-dimensional nonlinear Schr\\"odinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential.

  18. Darboux transformation of generalized coupled KdV soliton equation and its odd-soliton solutions

    Institute of Scientific and Technical Information of China (English)

    LIU Ping

    2008-01-01

    Based on the resulting Lax pairs of the generalized coupled KdV soliton equation,a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem.By using Darboux transformation,the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form.As an application,the first two cases are given.

  19. Soliton Management in Periodic Systems

    CERN Document Server

    Malomed, Boris A

    2006-01-01

    During the past ten years, there has been intensive development in theoretical and experimental research of solitons in periodic media. This book provides a unique and informative account of the state-of-the-art in the field. The volume opens with a review of the existence of robust solitary pulses in systems built as a periodic concatenation of very different elements. Among the most famous examples of this type of systems are the dispersion management in fiber-optic telecommunication links, and (more recently) photonic crystals. A number of other systems belonging to the same broad class of spatially periodic strongly inhomogeneous media (such as the split-step and tandem models) have recently been identified in nonlinear optics, and transmission of solitary pulses in them was investigated in detail. Similar soliton dynamics occurs in temporal-domain counterparts of such systems, where they are subject to strong time-periodic modulation (for instance, the Feshbach-resonance management in Bose-Einstein conde...

  20. Optical pulse compression using a nonlinear optical loop mirror constructed from dispersion decreasing fiber

    Institute of Scientific and Technical Information of China (English)

    CAO; Wenhua; LIU; Songhao

    2004-01-01

    A novel scheme to compress optical pulses is proposed and demonstrated numerically, which is based on a nonlinear optical loop mirror constructed from dispersion decreasing fiber (DDF). We show that, in contrast to the conventional soliton-effect pulse compression in which compressed pulses are always accompanied by pedestals and frequency chirps owning to nonlinear effects, the proposed scheme can completely suppress pulse pedestals and frequency chirps. Unlike the adiabatic compression technique in which DDF length must increase exponentially with input pulsewidth, the proposed scheme does not require adiabatic condition and therefore can be used to compress long pulses by using reasonable fiber lengths. For input pulses with peak powers higher than a threshold value, the compressed pulses can propagate like fundamental solitons. Furthermore, the scheme is fairly insensitive to small variations in the loop length and is more robust to higher-order nonlinear effects and initial frequency chirps than the adiabatic compression technique.

  1. Spatial solitons in photonic lattices with large-scale defects

    Institute of Scientific and Technical Information of China (English)

    Yang Xiao-Yu; Zheng Jiang-Bo; Dong Liang-Wei

    2011-01-01

    We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.

  2. Dirac-Point Solitons in Nonlinear Optical Lattices

    CERN Document Server

    Xie, Kang; Boardman, Allan D; Guo, Qi; Shi, Zhiwei; Jiang, Haiming; Hu, Zhijia; Zhang, Wei; Mao, Qiuping; Hu, Lei; Yang, Tianyu; Wen, Fei; Wang, Erlei

    2015-01-01

    The discovery of a new type of solitons occuring in periodic systems without photonic bandgaps is reported. Solitons are nonlinear self-trapped wave packets. They have been extensively studied in many branches of physics. Solitons in periodic systems, which have become the mainstream of soliton research in the past decade, are localized states supported by photonic bandgaps. In this Letter, we report the discovery of a new type of solitons located at the Dirac point beyond photonic bandgaps. The Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. These new solitons are sustained by the Dirac point rather than photonic bandgaps, thus provides a sort of advance in conceptual understanding over the traditional gap solitons. Apart from their theoretical impact within soliton theory, they have many potential uses because such solitons have dramatic stability characteristics and are possible in both Kerr material and photorefractive crystals that poss...

  3. Weak and strong interactions between dark solitons and dispersive waves

    CERN Document Server

    Oreshnikov, Ivan; Yulin, Alexey

    2015-01-01

    The effect of mutual interaction between dark solitons and dispersive waves is investigated numerically and analytically. The condition of the resonant scattering of dispersive waves on dark solitons is derived and compared against the results of numerical simulations. It is shown that the interaction with intense dispersive waves affects the dynamics of the soltons strongly changing their frequencies and accelerating or decelerating the solitons. It is also demonstrated that two dark solitons can form a cavity for dispersive weaves bouncing between the two dark solitons. The differences of the resonant scattering of the dispersive waves on the dark and bright solitons are discussed. In particular we demonstrate that two dark solitons and dispersive wave bouncing in between them create solitonic cavity with convex "mirrors" unlike the concave "mirror" in case of the bright solitons.

  4. The Pure Virtual Braid Group Is Quadratic

    CERN Document Server

    Lee, Peter

    2011-01-01

    If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra gr_I K need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a criterion which is equivalent to gr_I K being quadratic. We apply this criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic.

  5. Specialization of Quadratic and Symmetric Bilinear Forms

    CERN Document Server

    Knebusch, Manfred

    2010-01-01

    The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction. In addition to chapters on specialization theory, generic splitting t

  6. Quadratic stabilization of switched nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    DONG YaLi; FAN JiaoJiao; MEI ShengWei

    2009-01-01

    In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.

  7. Breathing dissipative solitons in optical microresonators

    CERN Document Server

    Lucas, Erwan; Guo, Hairun; Gorodetsky, Michael; Kippenberg, Tobias

    2016-01-01

    Dissipative solitons are self-localized structures resulting from a double balance between dispersion and nonlinearity as well as dissipation and a driving force. They occur in a wide variety of fields ranging from optics, hydrodynamics to chemistry and biology. Recently, significant interest has focused on their temporal realization in driven optical microresonators, known as dissipative Kerr solitons. They provide access to coherent, chip-scale optical frequency combs, which have already been employed in optical metrology, data communication and spectroscopy. Such Kerr resonator systems can exhibit numerous localized intracavity patterns and provide rich insights into nonlinear dynamics. A particular class of solutions consists of breathing dissipative solitons, representing pulses with oscillating amplitude and duration, for which no comprehensive understanding has been presented to date. Here, we observe and study single and multiple breathing dissipative solitons in two different microresonator platforms...

  8. Towards a Quantum Theory of Solitons

    CERN Document Server

    Dvali, Gia; Gruending, Lukas; Rug, Tehseen

    2015-01-01

    We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the soliton...

  9. Engineering optical soliton bistability in colloidal media

    CERN Document Server

    Matuszewski, Michal

    2010-01-01

    We consider a mixture consisting of two species of spherical nanoparticles dispersed in a liquid medium. We show that with an appropriate choice of refractive indices and particle diameters, it is possible to observe the phenomenon of optical soliton bistability in two spatial dimensions in a broad beam power range. Previously, this possibility was ruled out in the case of a single-species colloid. As a particular example, we consider the system of hydrophilic silica particles and gas bubbles generated in the process of electrolysis in water. The interaction of two soliton beams can lead to switching of the lower branch solitons to the upper branch, and the interaction of solitons from different branches is phase independent and always repulsive.

  10. Soliton concepts and the protein structure

    CERN Document Server

    Krokhotin, Andrei; Peng, Xubiao

    2011-01-01

    Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion, from a relatively small number of components. Here we propose to identify the modular building blocks of proteins with the dark soliton solution of a generalized discrete nonlinear Schrodinger equation. For this we show that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop specific parameters and we identify their possible values in Protein Data Bank. We show that with a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop, we cover over 90% of all proteins with experimental accuracy. We also present two examples that describe how the loop library can be employed both to model and to analyze the structure of folded proteins.

  11. Novel energy sharing collisions of multicomponent solitons

    Indian Academy of Sciences (India)

    T Kanna; K Sakkaravarthi; M Vijayajayanthi

    2015-11-01

    In this paper, we discuss the fascinating energy sharing collisions of multicomponent solitons in certain incoherently coupled and coherently coupled nonlinear Schrödinger-type equations arising in the context of nonlinear optics.

  12. Stability of solitons in PT-symmetric couplers

    CERN Document Server

    Driben, Rodislav

    2011-01-01

    Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").

  13. Solitons and spin transport in graphene boundary

    Indian Academy of Sciences (India)

    Kumar Abhinav; Vivek M Vyas; Prasanta K Panigrahi

    2015-11-01

    It is shown that in (2+1)-dimensional condensed matter systems, induced gravitational Chern–Simons (CS) action can play a crucial role for coherent spin transport in a finite geometry, provided zero-curvature condition is satisfied on the boundary. The role of the resultant KdV solitons is explicated. The fact that KdV solitons can pass through each other without interference, represent `resistanceless' spin transport.

  14. Spatial solitons in nonlinear liquid waveguides

    Indian Academy of Sciences (India)

    R Barillé; G Rivoire

    2001-11-01

    Spatial solitons are studied in a planar waveguide filled with nonlinear liquids. Spectral and spatial measurements for different geometries and input power of the laser beam show the influence of different nonlinear effects as stimulated scatterings on the soliton propagation and in particular on the beam polarization. The stimulated scattering can be used advantageously to couple the two polarization components. This effect can lead to multiple applications in optical switching.

  15. Solitons and spin transport in graphene boundary

    CERN Document Server

    Abhinav, Kumar; Panigrahi, Prasanta K

    2016-01-01

    It is shown that in (2+1)-dimensional condensed matter systems, induced gravitational Chern-Simons (CS) action can play a crucial role for coherent spin transport in a finite geometry, provided zero-curvature condition is satisfied on the boundary. The role of the resultant KdV solitons is explicated. The fact that KdV solitons can pass through each other without interference, represent 'resistanceless' spin transport.

  16. A Mass Formula for EYM Solitons

    CERN Document Server

    Corichi, A; Sudarsky, D; Corichi, Alejandro; Nucamendi, Ulises; Sudarsky, Daniel

    2001-01-01

    The recently introduced Isolated Horizon formalism, together with a simple phenomenological model for colored black holes is used to predict a formula for the ADM mass of the solitons of the EYM system in terms of horizon properties of black holes {\\it for all} values of the horizon area. In this note, this formula is tested numerically --up to a large value of the area-- for spherically symmetric solutions and shown to yield the known masses of the solitons.

  17. Structure of Solvable Quadratic Lie Algebras

    Institute of Scientific and Technical Information of China (English)

    ZHU Lin-sheng

    2005-01-01

    @@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.

  18. Radiotherapy treatment planning linear-quadratic radiobiology

    CERN Document Server

    Chapman, J Donald

    2015-01-01

    Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

  19. Quadratic stabilization for uncertain stochastic systems

    Institute of Scientific and Technical Information of China (English)

    Jun'e FENG; Weihai ZHANG

    2005-01-01

    This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems,where the uncertain matrix is norm bounded,and the external disturbance is a stochastic process.Two kinds of controllers are designed,which include state feedback case and output feedback case.The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities.The detailed design methods are presented.Numerical examples show the effectiveness of our results.

  20. A NEW INEXACT SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM

    Institute of Scientific and Technical Information of China (English)

    倪勤

    2002-01-01

    This paper represents an inexact sequential quadratic programming (SQP ) algorithm which can solve nonlinear programming (NLP ) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved.

  1. Solitons in one-dimensional photonic crystals

    CERN Document Server

    Mayteevarunyoo, Thawatchai

    2008-01-01

    We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of width L-D. The system is characterized by its structural "duty cycle", DC = D/L. In the case of the self-defocusing (SDF) intrinsic nonlinearity in the channels, one can predict new effects caused by competition between the linear trapping potential and the effective nonlinear repulsive one. Several species of solitons are found in the first two finite bandgaps of the SDF model, as well as a family of fundamental solitons in the semi-infinite gap of the system with the self-focusing nonlinearity. At moderate values of DC (such as 0.50), both fundamental and higher-order solitons populating the second bandgap of the SDF model suffer destabilization with the increase of the total power. Passing the destabilization point, the solitons assume a flat-top shape, while the shape of unstable solitons gets inverted, with loc...

  2. Models of few optical cycle solitons beyond the slowly varying envelope approximation

    Energy Technology Data Exchange (ETDEWEB)

    Leblond, H., E-mail: herve.leblond@univ-angers.fr [LUNAM University, Université d’Angers, Laboratoire de Photonique d’Angers, EA 4464, 2 Bd. Lavoisier, 49045 Angers Cedex 01 (France); Mihalache, D. [LUNAM University, Université d’Angers, Laboratoire de Photonique d’Angers, EA 4464, 2 Bd. Lavoisier, 49045 Angers Cedex 01 (France); Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125 Magurele (Romania); Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest (Romania)

    2013-02-15

    In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing field of the so-called extreme nonlinear optics. This review concentrates on theoretical studies performed in the past decade concerning the description of few optical cycle solitons beyond the slowly varying envelope approximation (SVEA). Here we systematically use the powerful reductive expansion method (alias multiscale analysis) in order to derive simple integrable and nonintegrable evolution models describing both nonlinear wave propagation and interaction of ultrashort (femtosecond) pulses. To this aim we perform the multiple scale analysis on the Maxwell–Bloch equations and the corresponding Schrödinger–von Neumann equation for the density matrix of two-level atoms. We analyze in detail both long-wave and short-wave propagation models. The propagation of ultrashort few-optical-cycle solitons in quadratic and cubic nonlinear media are adequately described by generic integrable and nonintegrable nonlinear evolution equations such as the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the complex modified Korteweg–de Vries equation, the sine–Gordon equation, the cubic generalized Kadomtsev–Petviashvili equation, and the two-dimensional sine–Gordon equation. Moreover, we consider the propagation of few-cycle optical solitons in both (1+1)- and (2+1)-dimensional physical settings. A generalized modified Korteweg–de Vries equation is introduced in order to describe robust few-optical-cycle dissipative solitons. We investigate in detail the existence and robustness of both linearly polarized and circularly polarized few-cycle solitons, that is, we also take into account the effect of the vectorial nature of the electric field. Some of these results concerning the systematic use of the reductive expansion method beyond the SVEA can be relatively easily extended to few

  3. Radiating subdispersive fractional optical solitons

    Energy Technology Data Exchange (ETDEWEB)

    Fujioka, J., E-mail: fujioka@fisica.unam.mx; Espinosa, A.; Rodríguez, R. F. [Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510 (Mexico); Malomed, B. A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

    2014-09-01

    It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

  4. Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

    Science.gov (United States)

    Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao

    2017-05-01

    Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.

  5. The explicit dependence of quadrat variance on the ratio of clump size to quadrat size.

    Science.gov (United States)

    Ferrandino, Francis J

    2005-05-01

    ABSTRACT In the past decade, it has become common practice to pool mapped binary epidemic data into quadrats. The resultant "quadrat counts" can then be analyzed by fitting them to a probability distribution (i.e., betabinomial). Often a binary form of Taylor's power law is used to relate the quadrat variance to the quadrat mean. The fact that there is an intrinsic dependence of such analyses on quadrat size and shape is well known. However, a clear-cut exposition of the direct connection between the spatial properties of the two-dimensional pattern of infected plants in terms of the geometry of the quadrat and the results of quadrat-based analyses is lacking. This problem was examined both empirically and analytically. The empirical approach is based on a set of stochastically generated "mock epidemics" using a Neyman-Scott cluster process. The resultant spatial point-patterns of infected plants have a fixed number of disease foci characterized by a known length scale (monodisperse) and saturated to a known disease level. When quadrat samples of these epidemics are fit to a beta-binomial distribution, the resulting measures of aggregation are totally independent of disease incidence and most strongly dependent on the ratio of the length scale of the quadrat to the length scale of spatial aggregation and to a lesser degree on disease saturation within individual foci. For the analytical approach, the mathematical form for the variation in the sum of random variates is coupled to the geometry of a quadrat through an assumed exponential autocorrelation function. The net result is an explicit equation expressing the intraquadrat correlation, quadrat variance, and the index of dispersion in terms of the ratio of the quadrat length scale to the correlative length scale.

  6. Multi-indexed Extensions of Soliton Potential and Extended Integer Solitons of KdV Equation

    CERN Document Server

    Ho, Choon-Lin

    2014-01-01

    We discover new infinite set of initial profiles of KdV solitons, which are both exactly solvable for the Schrodinger equation and for the Gel'fand-Levitan-Marchenko equation in the inverse scattering transform method of KdV equation. These new solutions are based on the multi-indexed extensions of the reflectionless soliton potential.

  7. The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

    Institute of Scientific and Technical Information of China (English)

    XU; Quan; TIAN; Qiang

    2005-01-01

    The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

  8. Relativistic quasi-solitons and embedded solitons with circular polarization in cold plasmas

    CERN Document Server

    Sánchez-Arriaga, G

    2016-01-01

    The existence of localized electromagnetic structures is discussed in the framework of the 1-dimensional relativistic Maxwell-fluid model for a cold plasma with immobile ions. New partially localized solutions are found with a finite-difference algorithm designed to locate numerically exact solutions of the Maxwell-fluid system. These solutions are called quasi-solitons and consist of a localized electromagnetic wave trapped in a spatially extended electron plasma wave. They are organized in families characterized by the number of nodes $p$ of the vector potential and exist in a continuous range of parameters in the $\\omega-V$ plane, where $V$ is the velocity of propagation and $\\omega$ is the vector potential angular frequency. A parametric study shows that the familiar fully localized relativistic solitons are special members of the families of partially localized quasi-solitons. Soliton solution branches with $p>1$ are therefore parametrically embedded in the continuum of quasi-solitons. On the other hand,...

  9. Diode-Pumped Soliton and Non-Soliton Mode-Locked Yb:GYSO Lasers

    Institute of Scientific and Technical Information of China (English)

    HE Jin-Ping; LIANG Xiao-Yan; LI Jin-Feng; ZHENG Li-He; SU Liang-Bi; XU Jun

    2011-01-01

    @@ Diode-pumped soliton and non-soliton mode-locked Yb:(Gd1-xYx,)2SiO5 (x=0.5) lasers are demonstrated.Pulsesas short as 1.4 ps are generated for the soliton mode-locked operation, with a pair of SF10 prisms as the negativedispersion elements.The central wavelength is 1056nm and the repetition rate is 48 MHz.For the non-solitonmode locking, the output power could achieve ~1.2W and the pulse width is about 20ps.The critical pulseenergy in the soliton-mode locked operation against the Q-switched mode locking is much lower than the criticalpulse energy in the non-soliton mode-locked operation

  10. Chladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids

    Science.gov (United States)

    Muñoz Mateo, A.; Brand, J.

    2014-12-01

    Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ , and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

  11. Vector solitons with locked and precessing states of polarization

    OpenAIRE

    Sergeyev, Sergey; Mou, Chengbo; Rozhin, Alex; Turitsyn, Sergei

    2012-01-01

    We demonstrate experimentally new families of vector solitons with locked and precessing states of polarization for fundamental and multipulse soliton operations in a carbon nanotube mode-locked fiber laser with anomalous dispersion laser cavity.

  12. Spatiotemporal dissipative solitons in two-dimensional photonic lattices.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S

    2008-11-01

    We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the truncated two-dimensional photonic lattice. We find the domains of existence and stability of such spatiotemporal dissipative solitons in the relevant parameter space, for both on-site and intersite lattice solitons. We show that the on-site solitons are stable in the whole domain of their existence, whereas most of the intersite solitons are unstable. We describe the scenarios of the instability-induced dynamics of dissipative solitons in two-dimensional lattices.

  13. Spinning solitons in cubic-quintic nonlinear media

    Indian Academy of Sciences (India)

    Lucian-Cornel Crasovan; Boris A Malomed; Dumitru Mihalache

    2001-11-01

    We review recent theoretical results concerning the existence, stability and unique features of families of bright vortex solitons (doughnuts, or ‘spinning’ solitons) in both conservative and dissipative cubic-quintic nonlinear media.

  14. BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors

    Science.gov (United States)

    Witt, Donald M.

    2011-04-01

    Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on

  15. Optical rogue waves and soliton turbulence in nonlinear fibre optics

    DEFF Research Database (Denmark)

    Genty, G.; Dudley, J. M.; de Sterke, C. M.

    2009-01-01

    We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....

  16. Nonlinear dynamics of soliton gas with application to "freak waves"

    Science.gov (United States)

    Shurgalina, Ekaterina

    2017-04-01

    So-called "integrable soliton turbulence" attracts much attention of scientific community nowadays. We study features of soliton interactions in the following integrable systems: Korteweg - de Vries equation (KdV), modified Korteweg - de Vries equation (mKdV) and Gardner equations. The polarity of interacted solitons dramatically influences on the process of soliton interaction. Thus if solitons have the same polarity the maximum of the wave field decreases during the process of nonlinear interactions as well statistical moments (skewness and kurtosis). In this case there is no abnormally large wave formation and this scenario is possible for all considered equation. Completely different results can be obtained for a soliton gas consisted of solitons with different polarities: such interactions lead to an increase of resulting impulse and kurtosis. Tails of distribution functions can grow significantly. Abnormally large waves (freak waves) appear in such solitonic fields. Such situations are possible just in case of mKdV and Gardner equations which admit the existence of bipolar solitons. New effect of changing a defect's moving direction in soliton lattices and soliton gas is found in the present study. Manifestation of this effect is possible as the result of negative phase shift of small soliton in the moment of nonlinear interaction with large solitons. It is shown that the effect of negative velocity is the same for KdV and mKdV equations and it can be found from the kinematic assumption without applying the kinetic theory. Averaged dynamics of the "smallest" soliton (defect) in a soliton gas, consisting of solitons with random amplitudes is investigated. The averaged criterion of velocity sign change confirmed by numerical simulation is obtained.

  17. Soliton tunneling with sub-barrier kinetic energies

    CERN Document Server

    González, J A; Guerrero, L E

    1999-01-01

    We investigate (theoretically and numerically) the dynamics of a soliton moving in an asymmetrical potential well with a finite barrier. For large values of the width of the well, the width of the barrier and/or the height of the barrier, the soliton behaves classically. On the other hand, we obtain the conditions for the existence of soliton tunneling with sub-barrier kinetic energies. We apply these results to the study of soliton propagation in disordered systems.

  18. Experiments on soliton motion in annular Josephson junctions

    DEFF Research Database (Denmark)

    Davidson, A.; Dueholm, B.; Pedersen, Niels Falsig

    1986-01-01

    We report here the results of an extensive experimental investigation of soliton dynamics in Josephson junctions of different annular geometries. The annular geometry is unique in that it allows for the study of undisturbed soliton motion as well as soliton–antisoliton collisons, since there are ...... for a single trapped soliton, and evidence linking the stability of the soliton to surface damping. Journal of Applied Physics is copyrighted by The American Institute of Physics....

  19. Soliton solutions of a generalized discrete KdV equation

    CERN Document Server

    Kanki, Masataka; Tokihiro, Tetsuji

    2012-01-01

    We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This phenomenon is intuitively understood from its ultradiscrete limit, where the system turns to the box ball system with a carrier. KEYWORDS: soliton, integrable equation, nonlinear system, discrete KdV equation, cellular automaton

  20. Peregrine soliton generation and breakup in standard telecommunications fiber.

    Science.gov (United States)

    Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Morin, Philippe; Fatome, Julien; Dudley, John M; Millot, Guy

    2011-01-15

    We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of nonideal initial conditions is studied through direct cutback measurements of the longitudinal evolution of the emerging soliton dynamics and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.

  1. Observation of Multimode Solitons in Few-Mode Fiber

    CERN Document Server

    Zhu, Zimu; Christodoulides, Demetrios N; Wise, Frank W

    2016-01-01

    We experimentally isolate and directly observe multimode solitons in few-mode graded-index fiber. By varying the input energy and modal composition of the launched pulse, we observe a continuous variation of multimode solitons with different spatiotemporal properties. They exhibit an energy-volume relation that is distinct from those of single-mode and fully spatiotemporal solitons.

  2. Oscillations of the soliton parameters in nonlinear interference phenomena

    Energy Technology Data Exchange (ETDEWEB)

    Tsoy, Eduard N. [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)], E-mail: etsoy@physic.uzsci.net; Sterke, C. Martijn de [Centre of Excellence for Ultrahigh-bandwidth Devices for Optical Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia)

    2008-03-10

    Applying the inverse scattering transform method, we show that a soliton modified by an amplitude or phase filter can evolve into several solitons. The oscillation period upon subsequent propagation follows from the wavenumbers of the emerging solitons and the radiation. Our results clarify spectral variations observed in recent supercontinuum experiments.

  3. Experimental Investigation of Trapped Sine-Gordon Solitons

    DEFF Research Database (Denmark)

    Davidson, A.; Dueholm, B.; Kryger, B.

    1985-01-01

    We have observed for the first time a single sine-Gordon soliton trapped in an annular Josephson junction. This system offers a unique possibility to study undisturbed soliton motion. In the context of perturbation theory, the soliton may be viewed as a relativistic particle moving under a uniform...

  4. Twin-Pulse Soliton Operation of a Fiber Laser

    Institute of Scientific and Technical Information of China (English)

    W.; S.; Man; H.; Y.; Tam

    2003-01-01

    We report on the experimental observation of a novel type of twin-pulse soliton in a passively mode-locked fiber ring laser. Twin-pulse soliton interaction in the laser cavity are also experimentally investigated and compared with those of the single pulse soliton.

  5. Stable rotating dipole solitons in nonlocal optical media

    DEFF Research Database (Denmark)

    Lopez-Aguayo, Servando; Desyatnikov, Anton S.; Kivshar, Yuri S.

    2006-01-01

    We reveal that nonlocality can provide a simplæe physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which we are known to be unstable in all types of realistic nonlinear...

  6. Spatiotemporal discrete surface solitons in binary waveguide arrays.

    Science.gov (United States)

    Mihalache, Dumitru; Mazilu, Dumitru; Kivshar, Yuri S; Lederer, Falk

    2007-08-20

    We study spatiotemporal solitons at the edge of a semi-infinite binary array of optical waveguides and, in particular, predict theoretically the existence of a novel type of surface soliton, the surface gap light bullets. We analyze the stability properties of these solitons in the framework of the continuous-discrete model of an array of two types of optical waveguides.

  7. Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

    DEFF Research Database (Denmark)

    Mak, Vicky; Thomadsen, Tommy

    2006-01-01

    This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

  8. Linear-quadratic control and quadratic differential forms for multidimensional behaviors

    NARCIS (Netherlands)

    Napp, D.; Trentelman, H.L.

    2011-01-01

    This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

  9. A Mixed-Binary Convex Quadratic Reformulation for Box-Constrained Nonconvex Quadratic Integer Program

    OpenAIRE

    Xia, Yong; Han, Ying-Wei

    2014-01-01

    In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.

  10. Binary classification posed as a quadratically constrained quadratic programming and solved using particle swarm optimization

    Indian Academy of Sciences (India)

    DEEPAK KUMAR; A G RAMAKRISHNAN

    2016-03-01

    Particle swarm optimization (PSO) is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The central idea is to use PSO to move in the direction towards optimal solution rather than searching the entire feasibleregion. Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or classification boundary for a data set. Our results on the Iris, Pima, Wine, Thyroid, Balance, Bupa, Haberman, and TAE datasets show that the proposed method works better than a neural network and the performance is close to that of a support vector machine

  11. Optical lattice trap for Kerr solitons

    Science.gov (United States)

    Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute

    2017-06-01

    We show theoretically and numerically that dichromatic pumping of a nonlinear microresonator by two continuous wave coherent optical pumps creates an optical lattice trap that results in the localization of intra-cavity Kerr solitons with soliton positions defined by the beat frequency of the two pumps. This phenomenon corresponds to the stabilization of the comb repetition rate. The locking of the second pump, through adiabatic tuning of its frequency, to the comb generated by the first pump allows transitioning to single-soliton states, manipulating the position of Kerr solitons in the cavity, and tuning the frequency comb repetition rate within the locking range. It also explains soliton crystal formation in resonators supporting a dispersive wave emitted as a result of higher-order group velocity dispersion or avoided mode crossing. We show that dichromatic pumping by externally stabilized pumps can be utilized for stabilization of microresonator-based optical frequency combs when the comb span does not cover an octave or a significant fraction thereof and standard self-referencing techniques cannot be employed. Our findings have significant ramifications for high-precision applications of optical frequency combs in spectrally pure signal generation, metrology, and timekeeping.

  12. Fast approximate quadratic programming for graph matching.

    Directory of Open Access Journals (Sweden)

    Joshua T Vogelstein

    Full Text Available Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs, we find that it efficiently achieves performance.

  13. Fast approximate quadratic programming for graph matching.

    Science.gov (United States)

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

  14. Quadratic Interpolation Algorithm for Minimizing Tabulated Function

    Directory of Open Access Journals (Sweden)

    E. A. Youness

    2008-01-01

    Full Text Available Problem statement: The problem of finding the minimum value of objective function, when we know only some values of it, is needed in more practical fields. Quadratic interpolation algorithms are the famous tools deal with this kind of these problems. These algorithms interested with the polynomial space in which the objective function is approximated. Approach: In this study we approximated the objective function by a one dimensional quadratic polynomial. This approach saved the time and the effort to get the best point at which the objective is minimized. Results: The quadratic polynomial in each one of the steps of the proposed algorithm, accelerate the convergent to the best value of the objective function without taking into account all points of the interpolation set. Conclusion: Any n-dimensional problem of finding a minimal value of a function, given by some values, can be converted to one dimensional problem easier in deal.

  15. Quadratic gravity: from weak to strong

    CERN Document Server

    Holdom, Bob

    2016-01-01

    More than three decades ago quadratic gravity was found to present a perturbative, renormalizable and asymptotically free theory of quantum gravity. Unfortunately the theory appeared to have problems with a spin-2 ghost. In this essay we revisit quadratic gravity in a different light by considering the case that the asymptotically free interaction flows to a strongly interacting regime. This occurs when the coefficient of the Einstein-Hilbert term is smaller than the scale $\\Lambda_{\\mathrm{QG}}$ where the quadratic couplings grow strong. Here QCD provides some useful insights. By pushing the analogy with QCD, we conjecture that the nonperturbative effects can remove the naive spin-2 ghost and lead to the emergence of general relativity in the IR.

  16. The Wiener maximum quadratic assignment problem

    CERN Document Server

    Cela, Eranda; Woeginger, Gerhard J

    2011-01-01

    We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time. Our approach also yields a polynomial time solution for the following problem from chemical graph theory: Find a tree that maximizes the Wiener index among all trees with a prescribed degree sequence. This settles an open problem from the literature.

  17. A CART extention using Quadratic Decision Borders

    DEFF Research Database (Denmark)

    Hartelius, Karsten

    1999-01-01

    In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...

  18. A CART extension using Quadratic Decision Borders

    DEFF Research Database (Denmark)

    Hartelius, Karsten

    1999-01-01

    In this article we put forward an extention to the hierarchical CART classification method which uses quadratic decision borders. The original CART applies univariate splits on individual variables as well as splits on combinations of variables to recursively partition the feature......-space into subsets which are successively more class-homogeneous. Guided by the fact that class-distributions in feature-space are very often hyper-elliptical shaped, we give an extension to the original CART which also uses quadratic shaped decision borders which can be modelled by a mean-vector and a dispersion...

  19. PSQP: Puzzle Solving by Quadratic Programming.

    Science.gov (United States)

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  20. Quintessence with quadratic coupling to dark matter

    CERN Document Server

    Boehmer, Christian G; Chan, Nyein; Lazkoz, Ruth; Maartens, Roy

    2009-01-01

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  1. Guises and disguises of quadratic divergences

    Energy Technology Data Exchange (ETDEWEB)

    Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  2. Indirect quantum tomography of quadratic Hamiltonians

    Energy Technology Data Exchange (ETDEWEB)

    Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

    2011-01-15

    A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

  3. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...

  4. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... on the simple observation that all functions in each component need the same extra parameters and thus a transitive closure is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity...

  5. On orthogonality preserving quadratic stochastic operators

    Energy Technology Data Exchange (ETDEWEB)

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  6. Discrete fractional Radon transforms and quadratic forms

    CERN Document Server

    Pierce, Lillian B

    2010-01-01

    We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from $\\ell^p$ to $\\ell^q$. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques from harmonic analysis, in particular Fourier transform methods and oscillatory integrals, as well as the number theoretic structure of quadratic forms, exponential sums, and theta functions, play key roles in the proof.

  7. Soliton models for thick branes

    Energy Technology Data Exchange (ETDEWEB)

    Peyravi, Marzieh [Ferdowsi University of Mashhad, Department of Physics, School of Sciences, Mashhad (Iran, Islamic Republic of); Riazi, Nematollah [Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Lobo, Francisco S.N. [Faculdade de Ciencias da Universidade de Lisboa, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal)

    2016-05-15

    In this work, we present new soliton solutions for thick branes in 4+1 dimensions. In particular, we consider brane models based on the sine-Gordon (SG), φ{sup 4} and φ{sup 6} scalar fields, which have broken Z{sub 2} symmetry in some cases and are responsible for supporting and stabilizing the thick branes. The origin of the symmetry breaking in these models resides in the fact that the modified scalar field potential may have non-degenerate vacua. These vacua determine the cosmological constant on both sides of the brane. We also study the geodesic equations along the fifth dimension, in order to explore the particle motion in the neighborhood of the brane. Furthermore, we examine the stability of the thick branes, by determining the sign of the w{sup 2} term in the expansion of the potential for the resulting Schroedinger-like equation, where w is the five-dimensional coordinate. It turns out that the φ{sup 4} brane is stable, while there are unstable modes for certain ranges of the model parameters in the SG and φ{sup 6} branes. (orig.)

  8. Soliton delivery of few-cycle optical gigawatt pulses in Kagome-lattice hollow-core photonic crystal fibers

    Science.gov (United States)

    Im, Song-Jin; Husakou, Anton; Herrmann, Joachim

    2010-08-01

    We study the delivery of few-cycle soliton-like pulses at 800 nm with gigawatt power or microjoule energy through a hollow-core kagome-lattice photonic crystal fiber over 1 m with preserved temporal and spectral shape. We show that with optimized pressure of the argon filling, 5 fs input pulses are compressed up to 2.5 fs after 20 cm and restore their shape after 1 m propagation.

  9. Optical Spatial Solitons and Their Interactions: Universality and Diversity.

    Science.gov (United States)

    Stegeman; Segev

    1999-11-19

    Spatial solitons, beams that do not spread owing to diffraction when they propagate, have been demonstrated to exist by virtue of a variety of nonlinear self-trapping mechanisms. Despite the diversity of these mechanisms, many of the features of soliton interactions and collisions are universal. Spatial solitons exhibit a richness of phenomena not found with temporal solitons in fibers, including effects such as fusion, fission, annihilation, and stable orbiting in three dimensions. Here the current state of knowledge on spatial soliton interactions is reviewed.

  10. Vector Dissipative Solitons in Graphene Mode Locked Fiber Lasers

    CERN Document Server

    Zhang, Han; Zhao, Luming; Bao, Qiaoliang; Loh, Kian Ping

    2010-01-01

    Vector soliton operation of erbium-doped fiber lasers mode locked with atomic layer graphene was experimentally investigated. Either the polarization rotation or polarization locked vector dissipative solitons were experimentally obtained in a dispersion-managed cavity fiber laser with large net cavity dispersion, while in the anomalous dispersion cavity fiber laser, the phase locked NLSE solitons and induced NLSE soliton were experimentally observed. The vector soliton operation of the fiber lasers unambiguously confirms the polarization insensitive saturable absorption of the atomic layer graphene when the light is incident perpendicular to its 2D atomic layer.

  11. Stabilization of spatiotemporal solitons in Kerr media by dispersive coupling

    CERN Document Server

    Kartashov, Yaroslav V; Konotop, Vladimir V; Lobanov, Valery E; Torner, Lluis

    2015-01-01

    We introduce a mechanism to stabilize spatiotemporal solitons in Kerr nonlinear media, based on the dispersion of linear coupling between the field components forming the soliton states. Specifically, we consider solitons in a two-core guiding structure with inter-core coupling dispersion (CD). We show that CD profoundly affects properties of the solitons, causing the complete stabilization of the otherwise highly unstable spatiotemporal solitons in Kerr media with focusing nonlinearity. We also find that the presence of CD stimulates the formation of bound states, which however are unstable.

  12. Matter-wave bright solitons in effective bichromatic lattice potentials

    Indian Academy of Sciences (India)

    Golam Ali Sekh

    2013-08-01

    Matter-wave bright solitons in bichromatic lattice potentials are considered and their dynamics for different lattice environments are studied. Bichromatic potentials are created from superpositions of (i) two linear optical lattices and (ii) a linear and a nonlinear optical lattice. Effective potentials are found for the solitons in both bichromatic lattices and a comparative study is done on the dynamics of solitons with respect to the effective potentials. The effects of dispersion on solitons in bichromatic lattices are studied and it is found that the dispersive spreading can be minimized by appropriate combinations of lattice and interaction parameters. Stability of nondispersive matter-wave solitons is checked from phase portrait analysis.

  13. Manakov Soliton Pairs in Biased Photovoltaic Photorefractive Crystals

    Institute of Scientific and Technical Information of China (English)

    侯春风; 杜春光; 阿不都热苏力; 李师群

    2002-01-01

    We study, theoretically, incoherently coupled screening-photovoltaic soliton pairs in biased photovoltaic photorefractive crystals. It is shown that when the total intensity of two coupled solitons is much lower than the effective dark irradiance, the coupled soliton equations reduce to the Manakov equations. The dark-dark, bright-bright and dark-bright soliton pair solutions of these Manakov equations are obtained under an appropriate external bias field and a photovoltaic field, and the characteristics of these Manakov soliton pairs are also discussed in detail.

  14. On the existence of stationary Ricci solitons

    CERN Document Server

    Figueras, Pau

    2016-01-01

    Previously the DeTurck 'trick' has been used to render the stationary Einstein's equation a well posed elliptic system that may be solved numerically by geometric flow or directly. Whilst in the static case for pure gravity with zero or negative cosmological constant there is a simple proof that solving the modified "harmonic" Einstein's equation leads to a solution of the original Einstein system - i.e. not a Ricci soliton - in the stationary case this argument no longer works. Here we provide a new argument that extends the static result to the case of stationary spacetimes that possess a "$t$-$\\phi$" reflection symmetry. Defining a "soliton charge" from the asymptotic behaviour of the solution, we show that this quantity is always non-positive. Provided asymptotic conditions are chosen such that this charge vanishes, then stationary solitons cannot exist.

  15. Solitonic axion condensates modeling dark matter halos

    Energy Technology Data Exchange (ETDEWEB)

    Castañeda Valle, David, E-mail: casvada@gmail.com; Mielke, Eckehard W., E-mail: ekke@xanum.uam.mx

    2013-09-15

    Instead of fluid type dark matter (DM), axion-like scalar fields with a periodic self-interaction or some truncations of it are analyzed as a model of galaxy halos. It is probed if such cold Bose–Einstein type condensates could provide a viable soliton type interpretation of the DM ‘bullets’ observed by means of gravitational lensing in merging galaxy clusters. We study solitary waves for two self-interacting potentials in the relativistic Klein–Gordon equation, mainly in lower dimensions, and visualize the approximately shape-invariant collisions of two ‘lump’ type solitons. -- Highlights: •An axion model of dark matter is considered. •Collision of axion type solitons are studied in a two dimensional toy model. •Relations to dark matter collisions in galaxy clusters are proposed.

  16. Tunneling Dynamics Between Atomic Bright Solitons

    CERN Document Server

    Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

    2016-01-01

    We investigate tunneling behavior between two bright solitons in a Bose-Einstein condensate with attractive contact interactions between atoms. The explicit tunneling properties including tunneling particles and oscillation period are described analytically, which indicates that the periodic tunneling form is a nonlinear Josephson type oscillation. The results suggest that the breathing behavior of solitons comes from the tunneling mechanism in an effective double-well potential, which is quite different from the modulational instability mechanism for Akhmediev breather and K-M breather. Furthermore, we obtain a phase diagram for two soliton interaction which admits tunneling property, particle-like property, interference property, and a resonant interaction case. The explicit conditions for them are clarified based on the defined critical distance $d_c$ and spatial interference period $D$.

  17. Introduction to soliton theory applications to mechanics

    CERN Document Server

    Munteanu, Ligia

    2005-01-01

    This monograph provides the application of soliton theory to solve certain problems selected from the fields of mechanics. The work is based of the authors' research, and on some specified, significant results existing in the literature. The present monograph is not a simple translation of its predecessor appeared in Publishing House of the Romanian Academy in 2002. Improvements outline the way in which the soliton theory is applied to solve some engineering problems. The book addresses concrete resolution methods of certain problems such as the motion of thin elastic rod, vibrations of initial deformed thin elastic rod, the coupled pendulum oscillations, dynamics of left ventricle, transient flow of blood in arteries, the subharmonic waves generation in a piezoelectric plate with Cantor-like structure, and some problems related to Tzitzeica surfaces. This comprehensive study enables the readers to make connections between the soliton physical phenomenon and some partical, engineering problems.

  18. Solitons in relativistic laser-plasma interactions

    Institute of Scientific and Technical Information of China (English)

    XIE Bai-song; DU Shu-cheng

    2007-01-01

    Single or/and multipeak solitons in plasma under relativistic electromagnetic field are reviewed.The incident electromagnetic field iS allowed to have a zero or/and nonzero initial constant amplitude.Some interesting numerical results are obtained that include a high-number multipeak laser pulse and single or/and low-number multipeak plasma wake structures.It is also shown that there exists a combination of soliton and oscillation waves for plasma wake field.Also,the electron density exhibits multi-caviton structure or the combination of caviton and oscillation.A complete eigenvalue spectrum of parameters is given wherein some higher peak numbers of multipeak electromagnetic solitons in the plasma are included.Moreover, some interesting scaling laws are presented for field energy via numerical approaches.Some implications of results are discussed.

  19. Conserved momenta of a ferromagnetic soliton

    Energy Technology Data Exchange (ETDEWEB)

    Tchernyshyov, Oleg, E-mail: olegt@jhu.edu

    2015-12-15

    Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether’s theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the spin Lagrangian and can be made arbitrary. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons. General considerations are illustrated on simple models of a domain wall in a ferromagnetic chain and of a vortex in a thin film.

  20. Soliton-like solution in quantum electrodynamics

    CERN Document Server

    Skoromnik, O D; Keitel, C H

    2016-01-01

    A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.

  1. Positons: slowly diminishing analogs of solitons

    CERN Document Server

    Matveev, V B

    2002-01-01

    The introduction to the theory of positons is presented. The positons are the remote-acting analogues of solitons and represent slowly diminishing and oscillating solitons of the nonlinear integrated equations of KdV type. The positon and soliton-positon solutions of the KdV equation were for the first time obtained and analyzed about 10 years ago and thereafter designed for a number of other models: mKdV, Toda chains, NSch, sn-Gordon equation and its lattice analog. By the proper selection of the scattering data the single positon and multipositon potentials are characterized by the remarkable property: the corresponding reflection coefficient is equal to zero and the transition coefficient is equal to one (the latter property, as it is known, has no place for the standard short-acting nonreflection potentials

  2. Single-qubit remote manipulation by magnetic solitons

    Energy Technology Data Exchange (ETDEWEB)

    Cuccoli, Alessandro, E-mail: cuccoli@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); CNISM – c/o Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Nuzzi, Davide, E-mail: nuzzi@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Vaia, Ruggero, E-mail: ruggero.vaia@isc.cnr.it [Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Verrucchi, Paola, E-mail: verrucchi@fi.infn.it [Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy)

    2016-02-15

    Magnetic solitons can constitute a means for manipulating qubits from a distance. This would overcome the necessity of directly applying selective magnetic fields, which is unfeasible in the case of a matrix of qubits embedded in a solid-state quantum device. If the latter contained one-dimensional Heisenberg spin chains coupled to each qubit, one can originate a soliton in a selected chain by applying a time-dependent field at one end of it, far from the qubits. The generation of realistic solitons has been simulated. When a suitable soliton passes by, the coupled qubit undergoes nontrivial operations, even in the presence of moderate thermal noise. - Highlights: • Proposal for the remote control of qubits coupled to a spin chain supporting solitons. • Traveling solitons can be generated on the chain by acting far from the qubit. • Suitable magnetic solitons can properly change the qubit state. • This qubit manipulation mechanism is shown to be resilient to thermal noise.

  3. Symmetry breaking of solitons in two-dimensional complex potentials

    CERN Document Server

    Yang, Jianke

    2014-01-01

    Symmetry breaking is reported for continuous families of solitons in the nonlinear Schr\\"odinger equation with a two-dimensional complex potential. This symmetry-breaking bifurcation is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, such symmetry breaking is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel stability properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenval...

  4. Massive WDM and TDM Soliton Transmission Systems : a ROSC Symposium

    CERN Document Server

    2002-01-01

    This book summarizes the proceedings of the invited talks presented at the “International Symposium on Massive TDM and WDM Optical Soliton Tra- mission Systems” held in Kyoto during November 9–12, 1999. The symposium is the third of the series organized by Research Group for Optical Soliton C- munications (ROSC) chaired by Akira Hasegawa. The research group, ROSC, was established in Japan in April 1995 with a support of the Japanese Ministry of Post and Telecommunications to promote collaboration and information - change among communication service companies, communication industries and academic circles in the theory and application of optical solitons. The symposium attracted enthusiastic response from worldwide researchers in the field of soliton based communications and intensive discussions were made. In the symposium held in 1997, new concept of soliton transmission based on dispersion management of optical fibers were presented. This new soliton is now called the dispersion managed soliton. The p...

  5. Single-mode dispersive waves and soliton microcomb dynamics

    Science.gov (United States)

    Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry

    2017-03-01

    Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.

  6. Temporal behaviour of open-circuit photovoltaic solitons

    Institute of Scientific and Technical Information of China (English)

    Zhang Mei-Zhi; Lu Ke-Qing; Cheng Guang-Hua; Li Ke-Hao; Zhang Yi-Qi; Zhang Yu-Hong; Zhang Yan-Peng

    2009-01-01

    Based on the time-dependent band-transport model in a photorefractive medium, dark open-circuit photovoltaic (PV) solitons are investigated both theoretically and experimentally. Compared with those of the time-independent models, our theoretical results revealed that quasi-steady-state and steady-state PV solitons can both be obtained.Our results also revealed that when r 1, however, the FWHM of solitons first decreases to a minimum before it increases to a constant value. Moreover, the FWHM of steady solitons decreases with increasing intensity ratio for r 1. We further observed dark PV solitons in experiments, and recorded their evolution. These results indicated that steady solitons can be observed at low optical power, while quasi-steady-state solitons can only be generated at higher optical power. Good agreement is found between theory and experiment.

  7. The Soliton Transmissions in Optical Fibers

    Directory of Open Access Journals (Sweden)

    Leos Bohac

    2010-01-01

    Full Text Available The objective of this paper is to familiarize readers with the basic analytical propagation model of short optical pulses in optical fiber. Based on this model simulation of propagation of the special type of pulse, called a soliton, will be carried out. A soliton transmission is especially attractive in the fiber optic telecommunication systems as it does not change a pulses shape during propagating right-down the fiber link to the receiver. The model of very short pulse propagation is based on the numerical solution of the nonlinear Schroedinger equation (NLSE, although in some specific cases it is possible to solve it analytically.

  8. Soliton blueshift in tapered photonic crystal fibers.

    Science.gov (United States)

    Stark, S P; Podlipensky, A; Russell, P St J

    2011-02-25

    We show that solitons undergo a strong blueshift in fibers with a dispersion landscape that varies along the direction of propagation. The experiments are based on a small-core photonic crystal fiber, tapered to have a core diameter that varies continuously along its length, resulting in a zero-dispersion wavelength that moves from 731 nm to 640 nm over the transition. The central wavelength of a soliton translates over 400 nm towards a shorter wavelength. This is accompanied by strong emission of radiation into the UV and IR spectral regions. The experimental results are confirmed by numerical simulation.

  9. Current-driven electron drift solitons

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, Ali, E-mail: aliahmad79@hotmail.com [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT) Islamabad (Pakistan); Saleem, H. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT) Islamabad (Pakistan)

    2013-12-09

    The soliton formation by the current-driven drift-like wave is investigated for heavier ion (such as barium) plasma experiments planned to be performed in future. It is pointed out that the sheared flow of electrons can give rise to short scale solitary structures in the presence of stationary heavier ions. The nonlinearity appears due to convective term in the parallel equation of motion and not because of temperature gradient unlike the case of low frequency usual drift wave soliton. This higher frequency drift-like wave requires sheared flow of electrons and not the density gradient to exist.

  10. Solitons on H bonds in proteins

    DEFF Research Database (Denmark)

    d'Ovidio, F.; Bohr, H.G.; Lindgård, Per-Anker

    2003-01-01

    system shows that the solitons are spontaneously created and are stable and moving along the helix axis. A perturbation on one of the three H-bond lines forms solitons on the other H bonds as well. The robust solitary wave may explain very long-lived modes in the frequency range of 100 cm(-1) which...... are found in recent x-ray laser experiments. The dynamics parameters of the Toda lattice are in accordance with the usual Lennard-Jones parameters used for realistic H-bond potentials in proteins....

  11. Synchrotron radiation of higher order soliton

    CERN Document Server

    Driben, Rodislav; Efimov, Anatoly

    2015-01-01

    We demonstrate radiation mechanism exhibited by higher order soliton. In a course of its evolution higher order soliton emits polychromatic radiation resulting in appearance of multipeak frequency comb like spectral band. The shape and spectral position of this band can be effectively controlled by the relative strength of the third order dispersion. An analytical description is completely corroborated by numerical simulations. An analogy between this radiation and the radiation of moving charges is presented. For longer pulses the described effect persists also under the action of higher order perturbations such as Raman and self-steepening.

  12. Multicomponent integrable wave equations: II. Soliton solutions

    Energy Technology Data Exchange (ETDEWEB)

    Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl

    2009-09-25

    The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.

  13. Dissipative plasmon solitons in graphene nanodisk arrays

    CERN Document Server

    Smirnova, Daria A; Smirnov, Lev A; Kivshar, Yuri S

    2014-01-01

    We study nonlinear modes in one-dimensional arrays of doped graphene nanodisks with Kerr-type nonlinear response in the presence of an external electric field. We present the theoretical model describing the evolution of the disks' polarizations, taking into account intrinsic graphene losses and dipole-dipole coupling between the graphene nanodisks. We reveal that this nonlinear system can support discrete dissipative scalar solitons of both longitudinal and transverse polarizations, as well as vector solitons composed of two mutually coupled polarization components. We demonstrate the formation of stable resting and moving localized modes under controlling guidance of the external driving field.

  14. Breather solitons in highly nonlocal media

    CERN Document Server

    Alberucci, Alessandro; Assanto, Gaetano

    2016-01-01

    We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science \\textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.

  15. Soliton form factors from lattice simulations

    CERN Document Server

    Rajantie, Arttu

    2010-01-01

    The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in 1+1-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model.

  16. "Compressed" Compressed Sensing

    CERN Document Server

    Reeves, Galen

    2010-01-01

    The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller number of samples is sufficient when there exists prior knowledge about the distribution of the unknown vector, or when only partial recovery is needed. An information-theoretic lower bound with connections to free probability theory and an upper bound corresponding to a computationally simple thresholding estimator are derived. It is shown that in certain cases (e.g. discrete valued vectors or large distortions) the number of samples can be decreased. Interestingly though, it is also shown that in many cases no reduction is possible.

  17. Examples of Sol-Solitons in the Pseudo-Riemannian case

    CERN Document Server

    Onda, Kensuke

    2011-01-01

    This paper provides a study of sol-solitons in the pseudo-Riemannian case. In the Riemannian case, all nontrivial homogeneous sol-soliton are expanding sol-solitons. In this paper, we obtain steady sol-solitons and shrinking sol-solitons in the Lorentzian setting.

  18. Test-assignment: a quadratic coloring problem

    NARCIS (Netherlands)

    Duives, Jelle; Lodi, Andrea; Malaguti, Enrico

    2013-01-01

    We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods bas

  19. Experimental results on quadratic assignment problem

    Directory of Open Access Journals (Sweden)

    N.P. Nikolov

    1999-08-01

    Full Text Available The paper presents experimental results on quadratic assignment problem. The "scanning area" method formulated for radioelectronic equipment design is applied. For all more complex tests ours results are better or coincident with the ones known in literature. Conclusion concerning the effectiveness of method are given.

  20. Quadratic Forms%二次型

    Institute of Scientific and Technical Information of China (English)

    谭亚茹

    2016-01-01

    The quadratic Higher Algebra is an important part of this paper, the definition of quadratic forms, introduces the second type of representation, and then describes how to use the allocation method, elementary transformation, orthogonal transformation method, etc. II second type into the standard form, and the second type of normal form, finally introduced posi-tive definite quadratic form and method for determining positive definite quadratic form.%二次型是高等代数的重要组成部分,本文从二次型的定义出发,介绍了二次型的表示方法,然后介绍了如何用配方法、初等变换法、正交变换法等将二次型化为标准形,以及二次型的规范形,最后介绍了正定二次型和判定正定二次型的方法。

  1. On Quadratic Programming with a Ratio Objective

    CERN Document Server

    Bhaskara, Aditya; Manokaran, Rajsekar; Vijayaraghavan, Aravindan

    2011-01-01

    Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \\sum_ij a_ij x_i x_j. QP captures many known combinatorial optimization problems and SDP techniques have given optimal approximation algorithms for many of these problems. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {-1,0,1}. The specific problem we study is: QP-Ratio: max_{-1,0,1}^n (x^T A x) / (x^T x). This objective function is a natural relative of several well studied problems. Yet, it is a good testbed for both algorithms and complexity because the techniques used for quadratic problems for the {-1,1} and {0,1} domains do not seem to carry over to the {-1,0,1} domain. We give approximation algorithms and evidence for the hardness of approximating the QP-Ratio problem. We consider an SDP relaxation obtained by adding constraints to the natural SDP relaxation for this problem and obtain an O(n^{2/7}) algorithm for...

  2. Distortion control of conjugacies between quadratic polynomials

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We use a new type of distortion control of univalent functions to give an alternative proof of Douady-Hubbard’s ray-landing theorem for quadratic Misiurewicz polynomials. The univalent maps arise from Thurston’s iterated algorithm on perturbation of such polynomials.

  3. Target manifold formation using a quadratic SDF

    Science.gov (United States)

    Hester, Charles F.; Risko, Kelly K. D.

    2013-05-01

    Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

  4. The GCD property and irreduciable quadratic polynomials

    Directory of Open Access Journals (Sweden)

    Saroj Malik

    1986-01-01

    Full Text Available The proof of the following theorem is presented: If D is, respectively, a Krull domain, a Dedekind domain, or a Prüfer domain, then D is correspondingly a UFD, a PID, or a Bezout domain if and only if every irreducible quadratic polynomial in D[X] is a prime element.

  5. Modulational instability in periodic quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Corney, Joel Frederick; Bang, Ole

    2001-01-01

    We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...

  6. Integration of the Quadratic Function and Generalization

    Science.gov (United States)

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  7. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    In this paper, we propose using realized range-based estimation to draw inference about the quadratic variation of jump-diffusion processes. We also construct a new test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test...

  8. Range-based estimation of quadratic variation

    DEFF Research Database (Denmark)

    Christensen, Kim; Podolskij, Mark

    This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient...

  9. The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons

    Science.gov (United States)

    Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.

    2016-04-01

    Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105

  10. Newton's cradles in optics: From to N-soliton fission to soliton chains

    CERN Document Server

    Driben, R; Yulin, A V; Skryabin, D V

    2013-01-01

    A mechanism for creating a Newton's cradle (NC) in nonlinear light wavetrains under the action of the third-order dispersion (TOD) is demonstrated. The formation of the NC structure plays an important role in the process of fission of higher-order N-solitons in optical fibers. After the splitting of the initial N--soliton into a nonuniform chain of fundamental quasi-solitons, the tallest one travels along the entire chain, through consecutive collisions with other solitons, and then escapes, while the remaining chain of pulses stays as a bound state, due to the radiation-mediated interaction between them. Increasing the initial soliton's order, $N$, leads to the transmission through, and release of additional solitons with enhanced power, along with the emission of radiation, which may demonstrate a broadband supercontinuum spectrum. The NC dynamical regime remains robust in the presence of extra perturbations, such as the Raman and self-steepening effects, and dispersions terms above the third order. It is d...

  11. Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect.

    Science.gov (United States)

    Flayac, H; Solnyshkov, D D; Shelykh, I A; Malpuech, G

    2013-01-04

    We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.

  12. Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

    Indian Academy of Sciences (India)

    M Akbari-Moghanjoughi; N Ahmadzadeh-Khosroshahi

    2011-08-01

    Oblique interaction of small- but finite-amplitude KdV-type electron-acoustic solitary excitations is examined in an unmagnetized two-electron-populated degenerate quantum electron–ion plasma in the framework of quantum hydrodynamics model using the extended Poincaré–Lighthill–Kuo (PLK) perturbation method. Critical plasma parameter is found to distinguish the types of solitons and their interaction phase-shifts. It is shown that, depending on the critical quantum diffraction parameter cr, both compressive and rarefactive solitary excitations may exist in this plasma and their collision phase-shifts can be either positive or negative for the whole range of collision angles 0 < θ < .

  13. Spin Waves in Magnetic Thin Films: New Types of Solitons and Electrical Control

    Science.gov (United States)

    Wang, Zihui

    New types of spin-wave solitons in magnetic thin films and the methods to control spin waves electrically are studied in this thesis. In the first part, the first observation of chaotic spin-wave solitons in yttrium iron garnet (YIG) thin film-based active feedback rings is presented. At some ring gain levels, one observes the self-generation of a single spin-wave soliton pulse in the ring. When the pulse circulates in the ring, its amplitude varies chaotically with time. The excitation of dark spin-wave envelope solitons in YIG thin film strips is also described. The formation of a pair of black solitons with a phase jump of 180° is observed for the first time. The excitation of bright solitons in the case of repulsive nonlinearity is also observed and is reproduced by a numerical simulation based on a high-order nonlinear Schrodinger equation. In the second part, the control of magnetization relaxation in ferromagnetic insulators via interfacial spin scattering is presented. In the experiments nanometer-thick YIG/Pt bi-layered structures are used, with the Pt layer biased by an electric voltage. The bias voltage produces a spin current across the Pt layer thickness due to the spin Hall effect. As this current scatters off the YIG surface, it exerts a torque on the YIG surface spins. This torque can reduce or increase the damping and thereby compress or broaden the ferromagnetic resonance linewidth of the YIG film, depending on the field/current configuration. The control of spin waves in a YIG thin film via interfacial spin scattering is also presented. In the experiments a 4.6-microm-thick YIG film strip with a 20-nm-thick Pt capping layer is used. A DC current pulse is applied to the Pt layer and produced a spin current across the Pt layer. As the spin current scatters off the YIG surface, it can either amplify or attenuate spin-wave pulses that travel in the YIG strip, depending on the current/field configuration.

  14. Quadratically constrained quadratic programs on acyclic graphs with application to power flow

    CERN Document Server

    Bose, Subhonmesh; Low, Steven H; Chandy, K Mani

    2012-01-01

    This paper proves that non-convex quadratically constrained quadratic programs have an exact semidefinite relaxation when their underlying graph is acyclic, provided the constraint set satisfies a certain technical condition. When the condition is not satisfied, we propose a heuristic to obtain a feasible point starting from a solution of the relaxed problem. These methods are then demonstrated to provide exact solutions to a richer class of optimal power flow problems than previously solved.

  15. String Solitons and T-duality

    CERN Document Server

    Bergshoeff, Eric A

    2011-01-01

    We construct for arbitrary dimensions a universal T-duality covariant expression for the Wess-Zumino terms of supersymmetric String Solitons in toroidally compactified string theories with 32 supercharges. The worldvolume fields occurring in the effective action of these String Solitons form either a vector or a tensor multiplet with 16 supercharges. We determine the dimensions of the conjugacy classes under T-duality to which these String Solitons belong. We do this in two steps. First, we determine the T-duality representations of the $p$-forms of maximal supergravities that contain the potentials that couple to these String Solitons. We find that these are p-forms, with D-4\\le p\\le 6 if D \\ge 6 and with D-4\\le p\\le D if D < 6, transforming in the antisymmetric representation of rank m=p+4-D\\le 4 of the T-duality symmetry SO(10-D,10-D). All branes support vector multiplets except when m=10-D. In that case the T-duality representation splits, for D<10, into a selfdual and anti-selfdual part, correspond...

  16. Solitons in nonlocal nonlinear media: Exact solutions

    DEFF Research Database (Denmark)

    Krolikowski, Wieslaw; Bang, Ole

    2001-01-01

    We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...

  17. Towards a quantum theory of solitons

    Energy Technology Data Exchange (ETDEWEB)

    Dvali, Gia [Arnold Sommerfeld Center for Theoretical Physics, LMU-München, Theresienstrasse 37, 80333 München (Germany); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München (Germany); Center for Cosmology and Particle Physics, Department of Physics, New York University, 4 Washington Place, New York, NY 10003 (United States); Gomez, Cesar [Arnold Sommerfeld Center for Theoretical Physics, LMU-München, Theresienstrasse 37, 80333 München (Germany); Instituto de Física Teórica, UAM–CSICm C–XVI Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gruending, Lukas, E-mail: Lukas.Gruending@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, LMU-München, Theresienstrasse 37, 80333 München (Germany); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München (Germany); Rug, Tehseen [Arnold Sommerfeld Center for Theoretical Physics, LMU-München, Theresienstrasse 37, 80333 München (Germany); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München (Germany)

    2015-12-15

    We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

  18. Towards a quantum theory of solitons

    Directory of Open Access Journals (Sweden)

    Gia Dvali

    2015-12-01

    Full Text Available We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

  19. A scattering theory of ultrarelativistic solitons

    NARCIS (Netherlands)

    Amin, M.A.; Lim, E.A.; Yang, I.S.

    2013-01-01

    We construct a perturbative framework for understanding the collision of solitons (more precisely, solitary waves) in relativistic scalar field theories. Our perturbative framework is based on the suppression of the space-time interaction area proportional to 1/(γv), where v is the relative velocity

  20. Ring vortex solitons in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Briedis, D.; Petersen, D.E.; Edmundson, D.;

    2005-01-01

    or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....

  1. Solitonic Information Transmission in General Relativity

    Institute of Scientific and Technical Information of China (English)

    SHANG Yu; WANG Gui-Dong; WU Xiao-Ning; WANG Shi-Kun; LAU Yun-Kau

    2007-01-01

    An exact solution of the vacuum Einstein's field equations is presented,in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation.On the basis of this exact solution,the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.

  2. Nonlinear soliton matching between optical fibers

    DEFF Research Database (Denmark)

    Agger, Christian; Sørensen, Simon Toft; Thomsen, Carsten L.

    2011-01-01

    In this Letter, we propose a generic nonlinear coupling coefficient, η2 NL ¼ ηjγ=β2jfiber2=jγ=β2jfiber1, which gives a quantitative measure for the efficiency of nonlinear matching of optical fibers by describing how a fundamental soliton couples from one fiber into another. Specifically, we use η...

  3. Kerr-Newman Electron as Spinning Soliton

    Science.gov (United States)

    Burinskii, Alexander

    2015-10-01

    Measurable parameters of the electron indicate that its background should be described by the Kerr-Newman (KN) solution. The spin/mass ratio of the electron is extreme large, and the black hole horizons disappear, opening a topological defect of space-time - the Kerr singular ring of Compton size, which may be interpreted as a closed fundamental string of low energy string theory. The singular and two-sheeted structure of the corresponding Kerr space has to be regularised, and we consider the old problem of regularising the source of the KN solution. As a development of the earlier Keres-Israel-Hamity-López model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: (1) the soliton forms a relativistically rotating bubble of Compton radius, which is filled by the oscillating Higgs field in a pseudo-vacuum state; (2) the boundary of the bubble forms a domain wall which interpolates between the internal flat background and the external exact Kerr-Newman (KN) solution; (3) the phase transition is provided by a system of chiral fields; (4) the vector potential of the external the KN solution forms a closed Wilson loop which is quantised, giving rise to a quantised spin of the soliton; (5) the soliton is bordered by a closed string, which is a part of the general complex stringy structure.

  4. Two-dimensional subwavelength plasmonic lattice solitons

    CERN Document Server

    Ye, F; Hu, B; Panoiu, N C

    2010-01-01

    We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detai

  5. Solitons in nucleon-nucleus collisions

    Energy Technology Data Exchange (ETDEWEB)

    Fogaca, D.A.; Navarra, F.S. [Sao Paulo Univ., SP (Brazil). Inst. de Fisica]. E-mail: hadron@terra.com.br

    2004-07-01

    Under certain conditions, the equations of non-relativistic hydrodynamics may provide a Korteweg-de Vries equation (KdV) which gives a soliton solution. We show that this solution and its properties are related to the microscopic features of the nuclear matter equation of state. (author)

  6. Solitons and Weakly Nonlinear Waves in Plasmas

    DEFF Research Database (Denmark)

    Pécseli, Hans

    1985-01-01

    Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...

  7. Internal mode of incoherent photovoltaic vector solitons

    Institute of Scientific and Technical Information of China (English)

    Zhang Bing-Zhi; Wang Hong-Cheng; She Wei-Long

    2007-01-01

    The internal modes of incoherent vector solitons (IVSs) in photovoltaic photorefractive materials are investigated in the framework of coupled nonlinear Schr(o)dinger equations. It is found that there is a pair of internal modes corresponding to a bright-bright IVS. The propagation dynamics of the bright-bright IVS perturbed by the internal modes is simulated by numerical method.

  8. Infrared Absorption in Acetanilide by Solitons

    DEFF Research Database (Denmark)

    Careri, G.; Buontempo, U.; Carta, F.;

    1983-01-01

    The infrared spectrum of acetanilide shows a new band that is red shifted from the main amide-I maximum by about 15 cm-1, the intensity of which increases at low temperature. It is suggested that this band may arise from the creation of amide-I solitons that are similar (but not identical) to those...

  9. Nonlinear structures of the Korteweg-de Vries and modified Korteweg-de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves

    Energy Technology Data Exchange (ETDEWEB)

    El-Tantawy, S. A., E-mail: samireltantawy@yahoo.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Moslem, W. M., E-mail: wmmoslem@hotmail.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Centre for Theoretical Physics, The British University in Egypt (BUE), El-Shorouk City, Cairo (Egypt)

    2014-05-15

    Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.

  10. Geometric Approaches to Quadratic Equations from Other Times and Places.

    Science.gov (United States)

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  11. Bidirectional soliton spectral tunneling effects in the regime of optical event horizon

    DEFF Research Database (Denmark)

    Gu, Jie; Guo, Hairun; Wang, Shaofei

    2015-01-01

    We study the cross-phase-modulation-induced soliton spectral shifting in the regime of the optical event horizon. The perturbed soliton to either red-shifting or blue-shifting is controllable, which could evoke bidirectional soliton spectral tunneling effects.......We study the cross-phase-modulation-induced soliton spectral shifting in the regime of the optical event horizon. The perturbed soliton to either red-shifting or blue-shifting is controllable, which could evoke bidirectional soliton spectral tunneling effects....

  12. Fission and Fusion of Solitons for the (1+1)-Dimensional Kupershmidt Equation

    Institute of Scientific and Technical Information of China (English)

    YING Jin-Ping

    2001-01-01

    By means of the heat conduction equation and the standard truncated Painlevé expansion, the (1+1) dimensional Kupershmidt equation is solved. Some significant exact multi-soliton solutions are given. Especially; for the interaction of the multi-solitons of the Kupershmidt equation, we find that a single (resonant) kink or bell soliton may be fissioned to several kink or bell solitons. Inversely, several kink or bell solitons may also be fused to one kink or bell soliton.

  13. On quadratic residue codes and hyperelliptic curves

    Directory of Open Access Journals (Sweden)

    David Joyner

    2008-01-01

    Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

  14. Higgsed Stueckelberg vector and Higgs quadratic divergence

    Directory of Open Access Journals (Sweden)

    Durmuş Ali Demir

    2015-01-01

    Full Text Available Here we show that, a hidden vector field whose gauge invariance is ensured by a Stueckelberg scalar and whose mass is spontaneously generated by the Standard Model Higgs field contributes to quadratic divergences in the Higgs boson mass squared, and even leads to its cancellation at one-loop when Higgs coupling to gauge field is fine-tuned. In contrast to mechanisms based on hidden scalars where a complete cancellation cannot be achieved, stabilization here is complete in that the hidden vector and the accompanying Stueckelberg scalar are both free from quadratic divergences at one-loop. This stability, deriving from hidden exact gauge invariance, can have important implications for modeling dark phenomena like dark matter, dark energy, dark photon and neutrino masses. The hidden fields can be produced at the LHC.

  15. Linear quadratic output tracking and disturbance rejection

    Science.gov (United States)

    Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza

    2011-08-01

    This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.

  16. Estimating quadratic variation using realized variance

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Shephard, N.

    2002-01-01

    This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimar......This paper looks at some recent work on estimating quadratic variation using realized variance (RV) - that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process...... have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd....

  17. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2002-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  18. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  19. Lambda-Lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, Olivier; Schultz, Ulrik Pagh

    2003-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  20. Lambda-lifting in Quadratic Time

    DEFF Research Database (Denmark)

    Danvy, O.; Schultz, U.P.

    2004-01-01

    Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

  1. Quaternion orders, quadratic forms, and Shimura curves

    CERN Document Server

    Alsina, Montserrat

    2004-01-01

    Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

  2. A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

    1999-01-01

    The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

  3. Elementary Components of the Quadratic Assignment Problem

    CERN Document Server

    Chicano, Francisco; Alba, Enrique

    2011-01-01

    The Quadratic Assignment Problem (QAP) is a well-known NP-hard combinatorial optimization problem that is at the core of many real-world optimization problems. We prove that QAP can be written as the sum of three elementary landscapes when the swap neighborhood is used. We present a closed formula for each of the three elementary components and we compute bounds for the autocorrelation coefficient.

  4. Cubic Lienard Equations with Quadratic Damping (Ⅱ)

    Institute of Scientific and Technical Information of China (English)

    Yu-quan Wang; Zhu-jun Jing

    2002-01-01

    Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.

  5. Characterization of a Quadratic Function in Rn

    Science.gov (United States)

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  6. Quadratic forms representing all odd positive integers

    CERN Document Server

    Rouse, Jeremy

    2011-01-01

    We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...

  7. Optimal Approximation of Quadratic Interval Functions

    Science.gov (United States)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  8. Steady-State Spatial Solitons in Low-Amplitude Regime in Biased Photorefractive-Photovoltaic Crystals

    Institute of Scientific and Technical Information of China (English)

    LU Keqing; ZHANG Yanpeng; TANG Tiantong; HOU Xun; WU Hongcai

    2001-01-01

    A theory of the space-charge field is improved in biased photorefractive-phorovoltaic crystals. Steady-state spatial solitons are obtained in the low-amplitude regime in biased photorefractive-photovoltaic crystals. When photovoltaic effect is neglected, these solitons are screening solitons, and their space-charge field is the space-charge field of screening solitons. When the external field is absent, these solitons are photovoltaic solitons for the closed or the open circuit and we also predict that gray solitons exist in photorefractive-photovoltaic crystals, and their space-charge field is the space-charge field of photovoltaic solitons.

  9. Gravitational two solitons in Levi-Cività spacetime

    Science.gov (United States)

    Igata, Takahisa; Tomizawa, Shinya

    2016-09-01

    Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Cività solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Cività background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one-solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.

  10. Gravitational two solitons in Levi-Civita spacetime

    CERN Document Server

    Igata, Takahisa

    2015-01-01

    Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Civita background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.

  11. Vector nematicons: Coupled spatial solitons in nematic liquid crystals

    Science.gov (United States)

    Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.

    2016-11-01

    Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrödinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case, bright soliton pairs have been found to exist provided their amplitudes satisfy a specific condition. In our analytical approach, focused on the defocusing regime, we rely on a multiscale expansion methods, which reveals the existence of dark-dark and antidark-antidark solitons, obeying an effective Korteweg-de Vries equation, as well as dark-bright solitons, obeying an effective Mel'nikov system. These pairs are discriminated by the sign of a constant that links all physical parameters of the system to the amplitude of the stable continuous wave solutions, and, much like the focusing case, the solitons' amplitudes are linked, leading to mutual guiding.

  12. 3D simulation for solitons used in optical fibers

    Science.gov (United States)

    Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.

    2016-12-01

    In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.

  13. Numerical stability of solitons waves through splices in optical fibers

    CERN Document Server

    de Oliveira, Camila Fogaça; Cirilo, Eliandro Rodrigues; Romeiro, Neyva Maria Lopes; Natti, Érica Regina Takano

    2015-01-01

    The propagation of soliton waves is simulated through splices in optical fibers, in which fluctuations of dielectric parameters occur. The mathematical modeling of these local fluctuations of dielectric properties of fibers was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter $\\beta$, a measure of the intensity of nonlinearity in the fiber. In order to verify whether the fluctuations of $\\beta$ parameter in the splices of the optical fiber generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter $\\beta$, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreas...

  14. Stability analysis for solitons in PT-symmetric optical lattices

    CERN Document Server

    Nixon, Sean; Yang, Jianke

    2012-01-01

    Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, the parameter range of stable solitons shrinks as new regions of instability appear. Thirdly, we investigate the nonlinear evolution of unstable PT solitons under perturbations, and show that the energy of perturbed solitons can grow unbounded even though the PT lattice is below the phase transition point.

  15. Single-mode dispersive waves and soliton microcomb dynamics

    CERN Document Server

    Yi, Xu; Zhang, Xueyue; Yang, Ki Youl; Vahala, Kerry

    2016-01-01

    Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton is shown to induce bistable behavior in the spectral and temporal properties of the soliton. Also, an operating point of enhanced repetition-rate stability is predicted and observed. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.

  16. Adiabatic theory of solitons fed by dispersive waves

    Science.gov (United States)

    Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, Shalva

    2016-09-01

    We consider scattering of low-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analog of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from quantum mechanics, we give a quantitative account of the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in the spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.

  17. Solitons in a chain of PT-invariant dimers

    CERN Document Server

    Suchkov, Sergey V; Dmitriev, Sergey V; Kivshar, Yuri S

    2011-01-01

    Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability...

  18. Dark-bright ring solitons in Bose-Einstein condensates

    Energy Technology Data Exchange (ETDEWEB)

    Stockhofe, J; Schmelcher, P [Zentrum fuer Optische Quantentechnologien, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Kevrekidis, P G [Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515 (United States); Frantzeskakis, D J, E-mail: jstockho@physnet.uni-hamburg.de, E-mail: kevrekid@math.umass.edu [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)

    2011-10-14

    We study dark-bright (DB) ring solitons in two-component Bose-Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration. (fast track communication)

  19. Soliton and kink jams in traffic flow with open boundaries.

    Science.gov (United States)

    Muramatsu, M; Nagatani, T

    1999-07-01

    Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.

  20. Chipscale optical frequency combs: from soliton physics to coherent communication (Conference Presentation)

    Science.gov (United States)

    Brasch, Victor; Geiselmann, Michael; Herr, Tobias; Lihachev, Grigoriy; Pfeiffer, Martin H. P.; Gorodetsky, Michael L.; Kippenberg, Tobias J.

    2016-04-01

    In our experiment we use silicon nitride waveguides embedded in silicon dioxide on a silicon chip. The cross section of the waveguide is approximately 1.8µm width by 0.8µm height and the ring resonator has a radius of 120µm. This resonator is coupled to a bus waveguide that is used to couple the continuous wave pump light into the resonator and the light from the resonator out again. The pump laser is an amplified diode laser which provides around 2W of pump power in the bus waveguide on the photonic chip. If the pump light is in resonance with one of the resonances of the resonator we can generate a frequency comb from the pump light via the Kerr nonlinearity of the material. The spacing in between the lines of the frequency comb is close to the free spectral range of the resonator, which is 190 GHz for the resonator used. By tuning the pump laser through the resonance and modulating the power of the pump light we can achieve a stable state with a pulsed-shape waveform circulating inside the microresonator. These states are known as dissipative Kerr soliton states and they are solutions to the Lugiato-Lefever equation, which describes the nonlinear physics of the system. So far they had been experimentally demonstrated in fiber-ring cavities as well as crystalline microresonators. The main benefits of these states for Kerr frequency combs is that they allow for low-noise but broadband frequency combs with low modulation in the spectrum. In our case we report a 3-dB bandwidth of 10THz which is equivalent to sub-30fs pulses inside the resonator. Because of the chosen geometry of the waveguide cross section we also observe an effect which is caused by higher-order dispersion. Higher-order dispersion are terms that describe the dispersion beyond the quadratic group velocity dispersion. In order for dissipative Kerr solitons to form, anomalous group velocity dispersion is required. If higher-order terms are present as well, the soliton can still exist but additional

  1. Perturbation-induced radiation by the Ablowitz-Ladik soliton.

    Science.gov (United States)

    Doktorov, E V; Matsuka, N P; Rothos, V M

    2003-12-01

    An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are calculated for linear damping and quintic perturbations.

  2. Production of strongly bound 39K bright solitons

    CERN Document Server

    Lepoutre, S; Boissé, A; Berthet, G; Salomon, G; Aspect, A; Bourdel, T

    2016-01-01

    We report on the production of 39 K matter-wave bright solitons, i.e., 1D matter-waves that propagate without dispersion thanks to attractive interactions. The volume of the soliton is studied as a function of the scattering length through three-body losses, revealing peak densities as high as $\\sim 5 \\times 10^{20} m^{-3}$. Our solitons, close to the collapse threshold, are strongly bound and will find applications in fundamental physics and atom interferometry.

  3. Supercontinuum generation with bright and dark solitons in optical fibers

    CERN Document Server

    Milián, Carles; Kudlinski, Alexandre; Skryabin, Dmitry V

    2016-01-01

    We study numerically and experimentally supercontinuum generation in optical fibers with dark and bright solitons simultaneously contributing into the spectral broadening and dispersive wave generation. We report a novel type of weak trapped radiation arising due to interaction of bright solitons with the dark soliton background. This radiation expresses itself as two pulses with the continuously shifting spectra constituting the short and long wavelength limits of the continuum. Our theoretical and experimental results are in good agreement.

  4. Stability of Bright Solitons in Bose-Einstein Condensates

    Institute of Scientific and Technical Information of China (English)

    YU Hui-You; YAN Jia-Ren; XIE Qiong-Tao

    2004-01-01

    We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Gross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schrodinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.

  5. The soliton properties of dipole domains in superlattices

    Institute of Scientific and Technical Information of China (English)

    张启义; 田强

    2002-01-01

    The formation and propagation of dipole domains in superlattices are studied both by the modified discrete driftmodel and by the nonlinear Schrodinger equation. The spatiotemporal distribution of the electric field and electrondensity are presented. The numerical results are compared with the soliton solutions of the nonlinear Schrodingerequation and analysed. It is shown that the numerical solutions agree with the soliton solutions of the nonlinearSchrodinger equation. The dipole electric-field domains in semiconductor superlattices have the properties of solitons.

  6. Protonic transport through solitons in hydrogen-bonded systems

    Science.gov (United States)

    Kavitha, L.; Jayanthi, S.; Muniyappan, A.; Gopi, D.

    2011-09-01

    We offer an alternative route for investigating soliton solutions in hydrogen-bonded (HB) chains. We invoke the modified extended tangent hyperbolic function method coupled with symbolic computation to solve the governing equation of motion for proton dynamics. We investigate the dynamics of proton transfer in HB chains through bell-shaped soliton excitations, which trigger the bio-energy transport in most biological systems. This solitonic mechanism of proton transfer could play functional roles in muscular contraction, enzymatic activity and oxidative phosphorylation.

  7. Soliton induced singularities in 2d gravity and their evaporation

    CERN Document Server

    Vaz, C; Vaz, Cenalo; Witten, Louis

    1995-01-01

    Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white hole, a timelike singularity and a black hole joined smoothly near the soliton center. When the cosmological constant is negative, the solutions describe two timelike singularities joined smoothly near the soliton center. We describe these spacetimes and examine their evaporation in the one loop approximation.

  8. Quadratic B-mode (QB-Mode) Ultrasonic Imaging with Coded Transmit Waveforms.

    Science.gov (United States)

    Cecchini, Daniele; Yao, Hui; Phukpattaranont, Pornchai; Ebbini, Emad

    2005-01-01

    In this paper, the use of coded transmit waveforms with post-beamforming nonlinear filtering of echo data in diagnostic ultrasound is presented. The nonlinear filter based on the second-order Volterra filter (SoVF) model separates the linear and quadratic echo components. The grayscale representation of the latter results in a new mode of imaging we refer to as quadratic B-mode (QB-mode). The use of chirp transmit waveforms in imaging contrast agents allows for nonlinear excitation of microbubble contrast agents (UCA) at a range of frequencies throughout the bandwidth of the transducer. The QB-mode image is shown to produce significant increase in UCA contrast over standard B-mode images from conventional and chirp excitation with and without compression. This contrast enhancement is achieved without loss in spatial resolution.

  9. Bäcklund Transformation and Soliton Solutions for a (3+1)-Dimensional Variable-Coefficient Breaking Soliton Equation

    Science.gov (United States)

    Zhao, Chen; Gao, Yi-Tian; Lan, Zhong-Zhou; Yang, Jin-Wei

    2016-09-01

    In this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method. N-soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.

  10. Coupled spatial multi-mode solitons in microcavity wires

    CERN Document Server

    Slavcheva, G; Pimenov, A

    2016-01-01

    A modal expansion approach is developed and employed to investigate and elucidate the nonlinear mechanism behind the multistability and formation of coupled multi-mode polariton solitons in microcavity wires. With pump switched on and realistic dissipation parameters, truncating the expansion up to the second-order wire mode, our model predicts two distinct coupled soliton branches: stable and ustable. Modulational stability of the homogeneous solution and soliton branches stability are studied. Our simplified 1D model is in remarkably good agreement with the full 2D mean-field Gross-Pitaevskii model, reproducing correctly the soliton existence domain upon variation of pump amplitude and the onset of multistability.

  11. Radiation by solitons due to higher-order dispersion

    DEFF Research Database (Denmark)

    Karpman, V.I.

    1993-01-01

    We consider the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution...... to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe...

  12. Bragg Fibers with Soliton-like Grating Profiles

    Directory of Open Access Journals (Sweden)

    Bugaychuk S.

    2016-01-01

    Full Text Available Nonlinear dynamical system corresponding to the optical holography in a nonlocal nonlinear medium with dissipation contains stable localized spatio-temporal states, namely the grid dissipative solitons. These solitons display a non-uniform profile of the grating amplitude, which has the form of the dark soliton in the reflection geometry. The transformation of the grating amplitude gives rise many new atypical effects for the beams diffracted on such grating, and they are very suitable for the fiber Brass gratings. The damped nonlinear Schrodinger equation is derived that describes the properties of the grid dissipative soliton.

  13. Interaction and resonance phenomena of multi-soliton

    Institute of Scientific and Technical Information of China (English)

    YANG Hong-juan; SHI Yu-ren; DUAN Wen-shan

    2006-01-01

    As is well known,Korteweg-de Vries equation is a typical one which has planar solitary wave.By considering higher order transverse disturbance to planar solitary waves,we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results.In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation,and theoretically find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitons.Three arbitrary amplitude soliton interaction of KP equation is also studied by numerical simulation,which can also results in resonance phenomena.

  14. Temporal development of open-circuit bright photovoltaic solitons

    Institute of Scientific and Technical Information of China (English)

    Zhang Lei; Lu Ke-Qing; Zhang Mei-Zhi; Liu Xue-Ming; Zhang Yan-Peng

    2008-01-01

    This paper investigates the temporal behaviour of open-circuit bright photovoltaic spatial solitons by using numerical techniques. It shows that when the intensity ratio of the soliton, the ratio between the soliton peak intensity and the dark irradiance, is small, the quasi-steady-state soliton width decreases monotonically with the increase of τ, where τis the parameter correlated with the time, that when the intensity ratio of the soliton is big, the quasi-steady-state soliton width decreases with the increase of τ and then increases with τ and that the formation time of the steady-state solitons is not correlated with the intensity ratio of the soliton. It finds that the local nonlinear effect increases with the photovoltaic field, which behaves as that the width of soliton beams is small and the self-focusing quasi-period is short. On the other hand, we also discuss that both the time and the temperature have an effect on the beam bending.

  15. Spiralling solitons and multipole localized modes in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan

    2007-01-01

    We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form.......We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different...

  16. Interaction of Nonlocal Incoherent White-Light Solitons

    Institute of Scientific and Technical Information of China (English)

    HUANG Chun-Fu; GUO Qi

    2007-01-01

    The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.

  17. Higher-order-mode fiber optimized for energetic soliton propagation.

    Science.gov (United States)

    Pedersen, Martin E V; Cheng, Ji; Charan, Kriti; Wang, Ke; Xu, Chris; Grüner-Nielsen, Lars; Jakobsen, Dan

    2012-08-15

    We describe the design optimization of a higher-order-mode (HOM) fiber for energetic soliton propagation at wavelengths below 1300 nm. A new HOM fiber is fabricated according to our design criteria. The HOM fiber is pumped at 1045 nm by an energetic femtosecond fiber laser. The soliton self-frequency shift process shifts the center wavelength of the soliton to 1085 nm. The soliton has a temporal duration of 216 fs and a pulse energy of 6.3 nJ. The demonstrated pulse energy is approximately six times higher than the previous record in a solid core fiber at wavelengths below 1300 nm.

  18. Modulation instability and solitons in two-color nematic crystals

    CERN Document Server

    Horikis, Theodoros P

    2016-01-01

    The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to soliton mutual guiding.

  19. Generation, compression, and propagation of pulse trains in the nonlinear Schrödinger equation with distributed coefficients.

    Science.gov (United States)

    Wang, Luyun; Li, Lu; Li, Zhonghao; Zhou, Guosheng; Mihalache, Dumitru

    2005-09-01

    The generalized nonlinear Schrödinger model with distributed dispersion, nonlinearity, and gain or loss is considered and the explicit, analytical solutions describing the dynamics of bright solitons on a continuous-wave background are obtained in quadratures. Then, the generation, compression, and propagation of pulse trains are discussed in detail. The numerical results show that solitons can be compressed by choosing the appropriate control fiber system, and pulse trains generated by modulation instability can propagate undistorsted along fibers with distributed parameters by controlling appropriately the energy of each pulse in the pulse train.

  20. Relationship Between Soliton-like Solutions and Soliton Solutions to a Class of Nonlinear Partial Differential Equations

    Institute of Scientific and Technical Information of China (English)

    LIU Chun-Ping; LING Zhi

    2005-01-01

    By using the generally projective Riccati equation method, a series of doubly periodic solutions (Jacobi elliptic function solution) for a class of nonlinear partial differential equations are obtained in a unified way. When the module m → 1, these solutions exactly degenerate to the soliton solutions of the equations. Then we reveal the relationship between the soliton-like solutions obtained by other authors and these soliton solutions of the equations.