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Sample records for singular soliton solutions

  1. The Singularity Structure of a Soliton Solution to the Higher-Dimensional Einstein Equations : Astrophysics and Relativity

    OpenAIRE

    Takahiro, AZUMA; Makoto, ENDO; Takao, KOIKAWA; Department of Mathematics, King's College London; Faculty of Liberal Arts, Dokkyo University; Department of Physics, Tokyo Metropolitan University

    1991-01-01

    We study a stationary and axisymmetric solution to the higher-dimensional Einstein equations and investigate its singularity structure. The solution consists of two solitons in the four-dimensional part (i.e., the Kerr solution) and n solitons in the extra dimensions. Naked singularities appear on the symmetry axis (z-axis) and/or at the event horizons of the Kerr solution. In a certain choice of integration constants there are solutions with regular event horizons.

  2. Singular and non-topological soliton solutions for nonlinear fractional differential equations

    Science.gov (United States)

    Ozkan, Guner

    2015-10-01

    In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space-time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.

  3. Singular 1-soliton and Periodic Solutions to the Nonlinear Fisher-Type Equation with Time-Dependent Coefficients

    Science.gov (United States)

    Ozkan, Guner; Ahmet, Bekir

    2016-04-01

    In this article, we establish exact solutions for the variable-coefficient Fisher-type equation. The solutions are obtained by the modified sine-cosine method and ansatz method. The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.

  4. Singular 1-soliton solution of the nonlinear variable-coefficient diffusion reaction and mKdV equations

    Science.gov (United States)

    Guner, Ozkan; Bekir, Ahmet; Unsal, Omer; Cevikel, Adem C.

    2017-01-01

    In this paper, we pay attention to the analytical method named, ansatz method for finding the exact solutions of the variable-coefficient modified KdV equation and variable coefficient diffusion-reaction equation. As a result the singular 1-soliton solution is obtained. These solutions are important for the explanation of some practical physical problems. The obtained results show that these methods provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. This method can be extended to solve other variable coefficient nonlinear partial differential equations.

  5. On soliton solutions of the Wu-Zhang system

    Directory of Open Access Journals (Sweden)

    Inc Mustafa

    2016-01-01

    Full Text Available In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.

  6. Singular solitons of generalized Camassa-Holm models

    International Nuclear Information System (INIS)

    Tian Lixin; Sun Lu

    2007-01-01

    Two generalizations of the Camassa-Holm system associated with the singular analysis are proposed for Painleve integrability properties and the extensions of already known analytic solitons. A remarkable feature of the physical model is that it has peakon solution which has peak form. An alternative WTC test which allowed the identifying of such models directly if formulated in terms of inserting a formed ansatz into these models. For the two models have Painleve property, Painleve-Baecklund systems can be constructed through the expansion of solitons about the singularity manifold. By the implementations of Maple, plentiful new type solitonic structures and some kink waves, which are affected by the variation of energy, are explored. If the energy is infinite in finite time, there will be a collapse in soliton systems by direct numerical simulations. Particularly, there are two collapses coexisting in our regular solitons, which occurred around its central regions. Simulation shows that in the bottom of periodic waves arises the non-zero parts of compactons and anti-compactons. We also get floating solitary waves whose amplitude is infinite. In contrary to which a finite-amplitude blow-up soliton is obtained. Periodic blow-ups are found too. Special kinks which have periodic cuspons are derived

  7. Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

    Science.gov (United States)

    Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj

    2017-11-01

    This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.

  8. The quasi-line soliton: Solutions to the Davey-Stewartson I equation

    OpenAIRE

    Arai, Takahito

    2012-01-01

    [Abstract] A periodic soliton is turned into a line soliton accordingly as a parameter point approaches to the boundary of the existing domain in the parameter space for a non-singular periodic soliton solution. We will call the periodic soliton solution with parameters of the neighborhood of the boundary a quasi-line soliton in this paper. We will examine that a periodic soliton turn into the line soliton as the parameter point of a periodic soliton approaches to the neighborhood of the boun...

  9. 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...... of these solitons and show their stability....

  10. Topological and non-topological soliton solutions to some time ...

    Indian Academy of Sciences (India)

    topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.

  11. Fundamental solutions of singular SPDEs

    Energy Technology Data Exchange (ETDEWEB)

    Selesi, Dora, E-mail: dora@dmi.uns.ac.rs [Department of Mathematics and Informatics, University of Novi Sad (Serbia)

    2011-07-15

    Highlights: > Fundamental solutions of linear SPDEs are constructed. > Wick-convolution product is introduced for the first time. > Fourier transformation maps Wick-convolution into Wick product. > Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. > Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P({omega}, D) Lozenge u(x, {omega}) = A(x, {omega}) are considered, where A is a singular generalized stochastic process and P({omega}, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A Lozenge I{sup Lozenge (-1)}, where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

  12. Fundamental solutions of singular SPDEs

    International Nuclear Information System (INIS)

    Selesi, Dora

    2011-01-01

    Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.

  13. One-soliton solutions from Laplace's seed

    Indian Academy of Sciences (India)

    One-soliton solutions of axially symmetric vacuum Einstein field equations are presented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the ...

  14. One-soliton solutions from Laplace's seed

    Indian Academy of Sciences (India)

    Abstract. One-soliton solutions of axially symmetric vacuum Einstein field equations are pre- sented in this paper. Two sets of Laplace's solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in ...

  15. Exact solutions and singularities in string theory

    International Nuclear Information System (INIS)

    Horowitz, G.T.; Tseytlin, A.A.

    1994-01-01

    We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail

  16. Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

    OpenAIRE

    Stalin, S.; Senthilvelan, M.

    2012-01-01

    In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different para...

  17. Multi-(Resonant-Soliton)-Soliton Solutions and Vortex-Like Solutions to Two- and Three-Dimensional Sine-Gordon Equations

    OpenAIRE

    Shozo, TAKENO; Department of Physics, Kyoto Technical University

    1982-01-01

    It is shown that for the two-and three-dimensional sine-Gordon equations there exist exact multi-(resonant-soliton)-soliton solutions and vortex-like solutions, in addition to exact multi-soliton and resonant-soliton solutions.

  18. Bright and dark soliton solutions of the (3+ 1)-dimensional ...

    Indian Academy of Sciences (India)

    In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin equation. By using two solitary wave ansatz in terms of sech p and tanh p functions, we obtain exact analytical bright and dark soliton solutions for the considered ...

  19. Soliton solutions of some nonlinear evolution equations with time ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 2. Soliton solutions of some nonlinear evolution equations with time-dependent coefficients ... In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schrödinger equation and (, ) equation with variable ...

  20. A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

    International Nuclear Information System (INIS)

    Chen, Yu-Zhu; Li, Wen-Du; Dai, Wu-Sheng

    2017-01-01

    We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

  1. A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)

    2017-12-15

    We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)

  2. Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation.

    Science.gov (United States)

    Wang, Shao-Fu

    2016-01-01

    The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking Soliton equation will be of great interest in future research.

  3. Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with δ-potential

    Science.gov (United States)

    Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga

    2018-03-01

    In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.

  4. Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas

    Science.gov (United States)

    Sindi, Cevat Teymuri; Manafian, Jalil

    2017-02-01

    In this paper, we extended the improved tan(φ/2)-expansion method (ITEM) and the generalized G'/G-expansion method (GGEM) proposed by Manafian and Fazli (Opt. Quantum Electron. 48, 413 (2016)) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). Moreover, we use of the improvement of the Exp-function method (IEFM) proposed by Jahani and Manafian (Eur. Phys. J. Plus 131, 54 (2016)) for obtaining solutions of NPDEs. The merit of the presented three methods is they can find further solutions to the considered problems, including soliton, periodic, kink, kink-singular wave solutions. This paper studies the quantum Zakharov-Kuznetsov (QZK) equation by the aid of the improved tan(φ/2)-expansion method, the generalized G'/G-expansion method and the improvement of the Exp-function method. Moreover, the 1-soliton solution of the modified QZK equation with power law nonlinearity is obtained by the aid of traveling wave hypothesis with the necessary constraints in place for the existence of the soliton. Comparing our new results with Ebadi et al. results (Astrophys. Space Sci. 341, 507 (2012)), namely, G'/G-expansion method, exp-function method, modified F-expansion method, shows that our results give further solutions. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.

  5. Classification of the line-soliton solutions of KPII

    Science.gov (United States)

    Chakravarty, Sarbarish; Kodama, Yuji

    2008-07-01

    In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

  6. Euler potentials for the MHD Kamchatnov-Hopf soliton solution

    NARCIS (Netherlands)

    Semenov, VS; Korovinski, DB; Biernat, HK

    2002-01-01

    In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf

  7. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    M. Nikuie

    2013-10-01

    Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

  8. Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System

    Directory of Open Access Journals (Sweden)

    Sheng Zhang

    2017-01-01

    Full Text Available Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. When n=1 and n=2, the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.

  9. Static and stationary multiple soliton solutions to the Einstein equations

    International Nuclear Information System (INIS)

    Letelier, P.S.

    1985-01-01

    The application of the Belinsky--Zakharov solution-generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd-number soliton solutions is investigated. These solutions represent solitonic perturbations of Euclidean metrics. The possibility of using instantons as seed solutions is also investigated. The one- and two-soliton solutions generated from a diagonal seed solution are studied. As an application, a unified derivation of some well-known static solutions, like the Schwarzschild metric and the Chazy--Curzon metric, as well as other new metrics is presented. By using these metrics as seed solutions, some known stationary solutions, like the Kerr-NUT metric, the double Kerr metric, and the rotating Weyl C-metric, as well as other new metrics are also derived in a unified way

  10. Brane Inflation, Solitons and Cosmological Solutions: I

    Energy Technology Data Exchange (ETDEWEB)

    Chen, P.

    2005-01-25

    In this paper we study various cosmological solutions for a D3/D7 system directly from M-theory with fluxes and M2-branes. In M-theory, these solutions exist only if we incorporate higher derivative corrections from the curvatures as well as G-fluxes. We take these corrections into account and study a number of toy cosmologies, including one with a novel background for the D3/D7 system whose supergravity solution can be completely determined. Our new background preserves all the good properties of the original model and opens up avenues to investigate cosmological effects from wrapped branes and brane-antibrane annihilation, to name a few. We also discuss in some detail semilocal defects with higher global symmetries, for example exceptional ones, that occur in a slightly different regime of our D3/D7 model. We show that the D3/D7 system does have the required ingredients to realize these configurations as non-topological solitons of the theory. These constructions also allow us to give a physical meaning to the existence of certain underlying homogeneous quaternionic Kahler manifolds.

  11. New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

    Science.gov (United States)

    Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

    2018-03-01

    In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

  12. Soliton solutions for some x-dependent nonlinear evolution equations

    International Nuclear Information System (INIS)

    Wang, Pan

    2014-01-01

    Under investigation in this paper are two x-dependent nonlinear evolution equations: the generalized x-dependent nonlinear Schrödinger (NLS) equation and the modified Korteweg–de Vries (KdV) equation. With the help of Hirota method and symbolic computation, the one- and two-soliton solutions have been obtained for the generalized x-dependent NLS and KdV equations. Propagation and evolution of one soliton have been investigated through the physical quantities of amplitude, width and velocity. The effects of the parameters in the equations on the interaction of two solitons have been studied analytically and graphically. (paper)

  13. Positive solutions for higher order singular p-Laplacian boundary ...

    Indian Academy of Sciences (India)

    of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. Keywords. Positive solution; singular BVPs; sufficient and necessary conditions; p-Laplacian equations. 1. Introduction. In this paper, we are concerned with higher order singular p-Laplacian boundary value problems. ⎧. ⎨. ⎩.

  14. N-Soliton Solutions of the Nonisospectral Generalized Sawada-Kotera Equation

    Directory of Open Access Journals (Sweden)

    Jian Zhou

    2014-01-01

    Full Text Available The soliton interaction is investigated based on solving the nonisospectral generalized Sawada-Kotera (GSK equation. By using Hirota method, the analytic one-, two-, three-, and N-soliton solutions of this model are obtained. According to those solutions, the relevant properties and features of line-soliton and bright-soliton are illustrated. The results of this paper will be useful to the study of soliton resonance in the inhomogeneous media.

  15. New types of exact quasi-soliton solutions in metamaterials

    International Nuclear Information System (INIS)

    Yang, Rongcao; Min, Xuemin; Tian, Jinping; Xue, Wenrui; Zhang, Wenmei

    2016-01-01

    We consider a generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in metamaterials (MMs) and present three new types of exact bright, dark, bright-grey quasi-solitons with a free constant associated with their amplitudes, pulse widths and formation conditions. Based on the Drude model, we analyze the existence regions and characteristics of these quasi-solitons in MMs. The results show that these bright and dark (grey) quasi-solitons can exist in wider regions of MMs and their intensities and pulse widths can be adjusted by choosing a suitable free constant. Furthermore, we take the third type of quasi-soliton solution as an example to numerically discuss the stabilities under slight perturbations of the frequency and the initial pulse width. The obtained results are helpful in exploring more solitary waves in MMs and providing a new reference for experimental verification. (paper)

  16. Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

    Science.gov (United States)

    Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

    2018-01-01

    In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

  17. Exact multi-line soliton solutions of noncommutative KP equation

    International Nuclear Information System (INIS)

    Wang, Ning; Wadati, Miki

    2003-01-01

    A method of solving noncommutative linear algebraic equations plays a key role in the extension of the ∂-bar -dressing on the noncommutative space-time manifold. In this paper, a solution-generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration. (author)

  18. Soliton solutions of some nonlinear evolution equations with time ...

    Indian Academy of Sciences (India)

    Dark and bright soliton; KdV equation; nonlinear Schrödinger equation; G(m, n) equation. PACS Nos 42.81.Dp; 42.65.Tg; 05.45.Yv. 1. Introduction. To find exact solutions of the nonlinear evolution equations (NLEEs) is one of the cen- tral themes in mathematics and physics. In recent years, many powerful methods have.

  19. Soliton solutions of some nonlinear evolution equations with time ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, we obtain exact soliton solutions of the modified KdV equation, inho- mogeneous nonlinear Schrödinger equation and G(m, n) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the ...

  20. Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability

    International Nuclear Information System (INIS)

    Gelash, A A; Zakharov, V E

    2014-01-01

    We describe a general N-solitonic solution of the focusing nonlinear Schrödinger equation in the presence of a condensate by using the dressing method. We give the explicit form of one- and two-solitonic solutions and study them in detail as well as solitonic atoms and degenerate solutions. We distinguish a special class of solutions that we call regular solitonic solutions. Regular solitonic solutions do not disturb phases of the condensate at infinity by coordinate. All of them can be treated as localized perturbations of the condensate. We find a broad class of superregular solitonic solutions which are small perturbations at a certain moment of time. Superregular solitonic solutions are generated by pairs of poles located on opposite sides of the cut. They describe the nonlinear stage of the modulation instability of the condensate and play an important role in the theory of freak waves. (invited article)

  1. Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation

    International Nuclear Information System (INIS)

    Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.

    1989-01-01

    The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs

  2. Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations

    Directory of Open Access Journals (Sweden)

    Laurent Delisle

    2012-08-01

    Full Text Available We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.

  3. Solitary wave solution to a singularly perturbed generalized Gardner ...

    Indian Academy of Sciences (India)

    2017-03-24

    Mar 24, 2017 ... which is one model in plasma physics and solid physics. [3]. Hamdi et al [4] obtained an exact solitary wave solution to eq. (1.2). They also derived three conserva- tion laws and three invariants of motion for eq. (1.2). [5]. Antonova and Biswas [6] exploited the soliton perturbation theory to eq. (1.2) with γ = 1.

  4. Solitons

    CERN Document Server

    Guo, Boling; Wang, Yu-Feng; Liu, Nan

    2018-01-01

    This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics.

  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...... solutions and the prediction of bound states of quadratic solitons....

  6. Periodic solutions to second-order indefinite singular equations

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2017-01-01

    Roč. 263, č. 1 (2017), s. 451-469 ISSN 0022-0396 Institutional support: RVO:67985840 Keywords : degree theory * indefinite singularity * periodic solution * singular differential equation Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.988, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022039617301134

  7. Uniqueness of singular solution of semilinear elliptic equation

    Indian Academy of Sciences (India)

    Nonhomogeneous semilinear elliptic equation; positive solutions; asymptotic behavior; singular ... a removable singular point of a solution of equation (1.1), the existence of the derivatives of the solution depends on the 'blow up' ..... On the other hand, for 0 <ε

  8. Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

    Science.gov (United States)

    Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

    2009-10-01

    In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

  9. Construction of Soliton-Cnoidal Wave Interaction Solution for the (2+1)-Dimensional Breaking Soliton Equation

    Science.gov (United States)

    Cheng, Wen-Guang; Li, Biao; Chen, Yong

    2015-05-01

    In this paper, the truncated Painlevé analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is difficult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus m = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, 11435005, and K.C. Wong Magna Fund in Ningbo University

  10. Soliton solutions of coupled nonlinear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Alagesan, T.; Chung, Y.; Nakkeeran, K.

    2004-01-01

    The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations

  11. The Zakharov system and its soliton solutions

    CERN Document Server

    Guo, Boling; Kong, Linghai; Zhang, Jingjun

    2016-01-01

    This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V. E. Zakharov – and in the course of those decades, many innovative achievements with major impacts on other research fields have been made. The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blow-up, low regularity, large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system. .

  12. Geometric characteristics of the solitonic solution in the case of finite density

    Science.gov (United States)

    Zhunussova, Zhanat; Dosmagulova, Karlygash

    2015-09-01

    Some exact solutions of nonlinear partial differential equations are widely investigated both mathematical and physical points of view. Physically interesting solution as solitonic is well known. Also solitonic solution have simple behavior in bumping and are stable. There are various methods for searching of these exact solutions.

  13. Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

    Science.gov (United States)

    Yu, Fajun

    2015-03-01

    We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

  14. Soliton-like solutions to the ordinary Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria

    2011-07-01

    In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

  15. A New Expression of Soliton Solution to the Ultradiscrete Toda Equation

    OpenAIRE

    Nagai, Hidetomo

    2008-01-01

    A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.

  16. Surface solitons in waveguide arrays: Analytical solutions.

    Science.gov (United States)

    Kominis, Yannis; Papadopoulos, Aristeidis; Hizanidis, Kyriakos

    2007-08-06

    A novel phase-space method is employed for the construction of analytical stationary solitary waves located at the interface between a periodic nonlinear lattice of the Kronig-Penney type and a linear or nonlinear homogeneous medium as well as at the interface between two dissimilar nonlinear lattices. The method provides physical insight and understanding of the shape of the solitary wave profile and results to generic classes of localized solutions having either zero or nonzero semi-infinite backgrounds. For all cases, the method provides conditions involving the values of the propagation constant of the stationary solutions, the linear refractive index and the dimensions of each part in order to assure existence of solutions with specific profile characteristics. The evolution of the analytical solutions under propagation is investigated for cases of realistic configurations and interesting features are presented such as their remarkable robustness which could facilitate their experimental observation.

  17. Soliton solutions for a quasilinear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Duchao Liu

    2013-12-01

    Full Text Available In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\\Delta_p u-\\frac{p}{2^{p-1}}u\\Delta_p(u^2=f(x,u $$ in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^{N}$ with Dirichlet boundary conditions.

  18. Analytical Solitons for Langmuir Waves in Plasma Physics with Cubic Nonlinearity and Perturbations

    Science.gov (United States)

    Zhou, Qin; Mirzazadeh, M.

    2016-09-01

    We presented an analytical study on dynamics of solitons for Langmuir waves in plasma physics. The mathematical model is given by the perturbed nonlinear Schrödinger equation with full nonlinearity and Kerr law nonlinearity. There are three techniques of integrability were employed to extract exact solutions along with the integrability conditions. The topological 1-soliton solutions, singular 1-soliton solutions, and plane wave solution were reported by Ricatti equation expansion approach and then the bright 1-soliton solution, singular 1-soliton solution, periodic singular solutions, and plane wave solution were derived with the help of trial solution method. Finally, based on the G'/G-expansion scheme, we obtained the hyperbolic function travelling wave solution, trigonometric function travelling wave solution, and plane wave solution.

  19. Solutions of dissimilar material singularity and contact problems

    International Nuclear Information System (INIS)

    Yang, Y.

    2003-09-01

    Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)

  20. Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates

    Energy Technology Data Exchange (ETDEWEB)

    Pinsker, Florian, E-mail: florian.pinsker@gmail.com

    2015-11-15

    In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.

  1. Solutions for a class of iterated singular equations

    Indian Academy of Sciences (India)

    Euler) equation as special cases. In [1] and [2], Altın studied radial type solutions of a class of singular partial differential equations of even order and obtained Lord Kelvin principle for this class of equations. In [5], all radial type solutions of eq.

  2. On Kaup-Kupershchmidt-type equations and their soliton solutions

    Science.gov (United States)

    Gerdjikov, V. S.

    2016-09-01

    We start with the Lax representation for the Kaup-Kupersschmidt equation (KKE). We outline the deep relation between the scalar Lax operator and the matrix Lax operators related to Kac-Moody algebras. Then we derive the MKdV equations gauge equivalent to the KKE. Next we outline the symmetry and the spectral properties of the relevant Lax operator. Using the dressing Zakharov-Shabat method we demonstrate that the MKdV and KKE have two types of one-soliton solutions and briefly comment on their properties.

  3. New exact solutions of the (2 + 1)-dimensional breaking soliton system via an extended mapping method

    International Nuclear Information System (INIS)

    Ma Songhua; Fang Jianping; Zheng Chunlong

    2009-01-01

    By means of an extended mapping method and a variable separation method, a series of solitary wave solutions, periodic wave solutions and variable separation solutions to the (2 + 1)-dimensional breaking soliton system is derived.

  4. Multi-kink solutions and soliton fission and fusion of Sharma-Tasso-Olver equation

    International Nuclear Information System (INIS)

    Chen Aihua

    2010-01-01

    From the Levi spectral problem, we obtain two basic Darboux transformations of the Sharma-Tasso-Olver equation. Then from the trivial seed solution, we obtain multi-kink solutions and soliton fission and fusion solutions of this equation.

  5. Trigonal curves and algebro-geometric solutions to soliton hierarchies I.

    Science.gov (United States)

    Ma, Wen-Xiu

    2017-07-01

    This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker-Akhiezer functions, and determine zeros and poles of the Baker-Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.

  6. On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations

    International Nuclear Information System (INIS)

    Zhestkov, S.V.

    2003-01-01

    The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)

  7. On the generation of magnetostatic solutions from gravitational two-soliton solutions of a stationary mass

    Energy Technology Data Exchange (ETDEWEB)

    Chaudhuri, A. [B.K.C. College, Department of Physics, Kolkata (India); Chaudhuri, S. [University of Burdwan, Department of Physics, Burdwan (India)

    2017-11-15

    In the paper, magnetostatic solutions of the Einstein-Maxwell field equations are generated from the gravitational two-soliton solutions of a stationary mass. Using the soliton technique of Belinskii and Zakharov (Sov Phys JETP 48:985, 1978, Sov Phys JETP 50:1, 1979), we construct diagonal two-soliton solutions of Einstein's gravitational field equations for an axially symmetric stationary space-time and investigate some properties of the generated stationary gravitational metric. Magnetostatic solutions corresponding to the generated stationary gravitational solutions are then constructed using the transformation technique of Das and Chaudhuri (Pramana J Phys 40:277, 1993). The mass and the dipole moment of the source are evaluated. In our analysis we make use of a second transformation (Chaudhuri in Pramana J Phys 58:449, 2002), probably for the first time in the literature, to generate magnetostatic solutions from the stationary gravitational two-soliton solutions which give us simple and straightforward expressions for the mass and the magnetic dipole moment. (orig.)

  8. Bilinear forms, N-soliton solutions and soliton interactions for a fourth-order dispersive nonlinear Schrödinger equation in condensed-matter physics and biophysics

    International Nuclear Information System (INIS)

    Liu, Rong-Xiang; Tian, Bo; Liu, Li-Cai; Qin, Bo; Lü, Xing

    2013-01-01

    In this paper we investigate a fourth-order dispersive nonlinear Schrödinger equation, which governs the dynamics of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction in condensed-matter physics as well as the alpha helical proteins with higher-order excitations and interactions in biophysics. Beyond the existing constraint, upon the introduction of an auxiliary function, bilinear forms and N-soliton solutions are constructed with the Hirota method. Asymptotic analysis on the two-soliton solutions indicates that the soliton interactions are elastic. Soliton velocity varies linearly with the coefficient of discreteness and higher-order magnetic interactions. Bound-state solitons can also exist under certain conditions. Period of a bound-state soliton is inversely correlated to the coefficient of discreteness and higher-order magnetic interactions. Interactions among the three solitons are all pairwise elastic

  9. The Rational Solutions and Quasi-Periodic Wave Solutions as well as Interactions of N-Soliton Solutions for 3 + 1 Dimensional Jimbo-Miwa Equation

    Directory of Open Access Journals (Sweden)

    Hongwei Yang

    2016-01-01

    Full Text Available The exact rational solutions, quasi-periodic wave solutions, and N-soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant solution which is a special form of the N-soliton solutions. At last, the interactions of the solitons are shown with the aid of N-soliton solutions.

  10. Solitary wave solution to a singularly perturbed generalized Gardner ...

    Indian Academy of Sciences (India)

    2015-11-27

    Home; Journals; Pramana – Journal of Physics; Volume 88; Issue 4. Solitary wave solution to a singularly perturbed generalized ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: ...

  11. Singularity free non-rotating cosmological solutions for perfect fluids ...

    Indian Academy of Sciences (India)

    Singularity free cosmological solutions of the type stated in the title known so far are of a very special class and have the following characteristics: (a) The space time is cylindrically symmetric. (b) In case the metric is diagonal, the μ's are of the form μ = a function of time multiplied by a function of the radial coordinate.

  12. Positive solutions for higher order singular p-Laplacian boundary ...

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 118; Issue 2. Positive Solutions for Higher Order Singular -Laplacian Boundary Value Problems. Guoliang Shi Junhong Zhang ... Guoliang Shi1 Junhong Zhang1. Department of Mathematics, Tianjin University, Tianjin 300072, People's Republic of China ...

  13. Slowly growing solutions of singular linear functional differential systems

    Czech Academy of Sciences Publication Activity Database

    Pylypenko, V.; Rontó, András

    2012-01-01

    Roč. 285, 5-6 (2012), s. 727-743 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : functional differential equation * singular Cauchy problem * slowly growing solution Subject RIV: BA - General Mathematics Impact factor: 0.576, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/ mana .201000014/abstract

  14. Existence of solutions to singular fractional differential systems with impulses

    Directory of Open Access Journals (Sweden)

    Xingyuan Liu

    2012-11-01

    Full Text Available By constructing a weighted Banach space and a completely continuous operator, we establish the existence of solutions for singular fractional differential systems with impulses. Our results are proved using the Leray-Schauder nonlinear alternative, and are illustrated with examples.

  15. Positive solutions of singular boundary value problem of negative ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Thus we complete the proof of. Theorem 2.2. Acknowledgement. This work is supported in part by the NSF(Youth) of Shandong Province and NNSF of. China. References. [1] Fink A M, Gatica J A, Hernandez G E and Waltman P, Approximation of solutions of singular second order boundary value problems, SIAM J. Math.

  16. Singularity free non-rotating cosmological solutions for perfect fluids ...

    Indian Academy of Sciences (India)

    Again an analysis leads to the Senovilla solution with. = ½. ¿ i.e.. Ф = ½. ¿p. 6. Conclusion. Our motivation was to examine whether non-singular non-rotating perfect fluid (with Ф = ) cosmologies exist besides those already discovered and presented in the literature. We have not been able to give an unequivocal answer but ...

  17. Trigonal curves and algebro-geometric solutions to soliton hierarchies II.

    Science.gov (United States)

    Ma, Wen-Xiu

    2017-07-01

    This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi coordinates associated with Lax pairs, upon determining the Riemann theta function representations of the Baker-Akhiezer functions, and generate algebro-geometric solutions to soliton hierarchies in terms of the Riemann theta functions, through observing asymptotic behaviours of the Baker-Akhiezer functions. We emphasize that we analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.

  18. Reduction and New Explicit Solutions of (2+1)-Dimensional Breaking Soliton Equation

    Science.gov (United States)

    Tian, Ying-Hui; Chen, Han-Lin; Liu, Xi-Qiang

    2006-01-01

    By applying the Lie group method, the (2+1)-dimensional breaking soliton equation is reduced to some (1+1)-dimensional nonlinear equations. Based upon some new explicit solutions of the (2+1)-dimensional breaking soliton equation are obtained.

  19. Soliton solutions describing charged particle propagation in a system with self-induction

    International Nuclear Information System (INIS)

    Mitropol'skij, I.A.; Shuvaev, A.G.

    1991-01-01

    Soliton solutions of the equations describing charged particle motion in an inductive feedback system are derived for quantum and classical cases. Possible existence of soliton bound states is shown. Conditions of longitudinal focusing of particles which propagate at different initial velocities in a nonlinear medium are discussed

  20. 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

  1. Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation

    Science.gov (United States)

    Wang, Ling; Dong, Zhong-Zhou

    2008-10-01

    By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation.

  2. Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation

    International Nuclear Information System (INIS)

    Wang Ling; Dong Zhongzhou

    2008-01-01

    By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation

  3. Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation

    Directory of Open Access Journals (Sweden)

    Hai-Feng Zhang

    2013-01-01

    Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.

  4. Holomorphic Vector Bundles Corresponding to some Soliton Solutions of the Ward Equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, Xiujuan, E-mail: yzzhuxiujuan@sina.com [Jiangsu Second Normal University, School of Mathematics and Information Technology (China)

    2015-12-15

    Holomorphic vector bundles corresponding to the static soliton solution of the Ward equation were explicitly presented by Ward in terms of a meromorphic framing. Bundles (for simplicity, “bundle” is to be taken throughout to mean “holomorphic vector bundle”) corresponding to all Ward k-soliton solutions whose extended solutions have only simple poles, and some Ward 2-soliton solutions whose extended solutions have only a second-order pole, were explicitly described by us in a previous paper. In this paper, we go on to present some bundles corresponding to soliton-antisoliton solutions of the Ward equation, and Ward 3-soliton solutions whose extended solutions have a simple pole and a double pole. To give some more interpretation of the bundles, we study the second Chern number of the corresponded bundles and find that it can be obtained directly from the patching matrices. We also point out some information about bundles corresponding to Ward soliton solutions whose extended solutions have general pole data at the end of the paper.

  5. Solitary wave solution to a singularly perturbed generalized Gardner ...

    Indian Academy of Sciences (India)

    2017-03-24

    Mar 24, 2017 ... This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation .... will be used in §3 for our purpose. For convenience, we use a version of this theory due to Jones [2]. For the system. { x (t) = f (x, y, ε), y (t) = εg(x, y, ε),. (2.1) where x ∈ Rn, y ...

  6. Positive solutions for higher order singular p-Laplacian boundary ...

    Indian Academy of Sciences (India)

    (1.4). The singular or nonsingular fourth-order boundary value problems (1.4) have been exten- sively studied by many authors [1,2,6,7,10,13–15]. Shi and Chen [10,11] gave the sufficient and necessary conditions for the existence of positive solutions to superlinear problem (1.4) by the fixed point theorem in cones when 1 ...

  7. Relaxation periodic solutions of one singular perturbed system with delay

    Science.gov (United States)

    Kashchenko, A. A.

    2017-12-01

    In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.

  8. Canard solutions of two-dimensional singularly perturbed systems

    Energy Technology Data Exchange (ETDEWEB)

    Chen Xianfeng [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)]. E-mail: chenxf@sjtu.edu.cn; Yu Pei [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Department of Applied Mathematics, University of Western Ontario London, Ont., N6A 5B7 (Canada); Han Maoan [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China); Zhang Weijiang [Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 (China)

    2005-02-01

    In this paper, some new lemmas on asymptotic analysis are established. We apply an asymptotic method to study generalized two-dimensional singularly perturbed systems with one parameter, whose critical manifold has an m-22 th-order degenerate extreme point. Certain sufficient conditions are obtained for the existence of canard solutions, which are the extension and correction of some existing results. Finally, one numerical example is given.

  9. The soliton solution of the PHI24 field theory in the Hartree approximation

    International Nuclear Information System (INIS)

    Altenbokum, M.

    1984-01-01

    In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

  10. Lump Solutions and Resonance Stripe Solitons to the (2+1-Dimensional Sawada-Kotera Equation

    Directory of Open Access Journals (Sweden)

    Xian Li

    2017-01-01

    Full Text Available Based on the symbolic computation, a class of lump solutions to the (2+1-dimensional Sawada-Kotera (2DSK equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

  11. New multi-soliton solutions for generalized Burgers-Huxley equation

    Directory of Open Access Journals (Sweden)

    Liu Jun

    2013-01-01

    Full Text Available The double exp-function method is used to obtain a two-soliton solution of the generalized Burgers-Huxley equation. The wave has two different velocities and two different frequencies.

  12. Modulation instability analysis of modify unstable nonlinear schrodinger dynamical equation and its optical soliton solutions

    Directory of Open Access Journals (Sweden)

    Muhammad Arshad

    Full Text Available The nonlinear Schrödinger equations (NLSEs describe the promulgation of ultra-short pluse in optical fibers. The modify unstable nonlinear Schrödinger equation (mUNLSE is a universal equation of the class of nonlinear integrable systems in NLSEs, which governs certain instabilities of modulated wave-trains. This equation also describes the time evolution of disturbances in marginally stable or unstable media. In the current work, the aim is to investigate the mUNLSE analytically by utilizing proposed modified extended mapping method. New exact solutions are constructed in the different form such as exact dark soliton, exact bright soliton, bright-dark soliton, solitary wave, elliptic function in different form and periodic solutions of mUNLSE. Furthermore, we also present the formation conditions of the bright soliton and dark soliton of this equation. The modulation instability analysis is implemented to discuss the stability analysis of the attained solutions and the movement role of the waves is examined, which confirms that all constructed solutions are exact and stable. Keywords: Modify unstable nonlinear schrödinger equation, Modified extended mapping method, bright and dark solitons, Solitary wave solutions, Elliptic function solutions, periodic solutions

  13. Soliton solutions and their stability for the flow of relativistic fluids through channels

    Science.gov (United States)

    Lerche, I.; Wiita, P. J.

    1980-01-01

    The flow of a perfect relativistic fluid through channels of various cross-sections is considered with reference to models of radio galaxies. Soliton-like solutions are found and their topologies are discussed. The calculations show that these solutions are unstable. It is suggested that under realistic astrophysical conditions the growth rate of the instabilities is so slow that soliton-type blobs may persist for a significant time.

  14. Thermodynamical description of stationary, asymptotically flat solutions with conical singularities

    International Nuclear Information System (INIS)

    Herdeiro, Carlos; Rebelo, Carmen; Radu, Eugen

    2010-01-01

    We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and nonconnected event horizons, using the thermodynamical description recently proposed in [C. Herdeiro, B. Kleihaus, J. Kunz, and E. Radu, Phys. Rev. D 81, 064013 (2010).]. The examples considered are the double-Kerr solution, the black ring rotating in either S 2 or S 1 , and the black Saturn, where the balance condition is not imposed for the latter two solutions. We show that not only the Bekenstein-Hawking area law is recovered from the thermodynamical description, but also the thermodynamical angular momentum is the Arnowitt-Deser-Misner angular momentum. We also analyze the thermodynamical stability and show that, for all these solutions, either the isothermal moment of inertia or the specific heat at constant angular momentum is negative, at any point in parameter space. Therefore, all these solutions are thermodynamically unstable in the grand canonical ensemble.

  15. Soliton solutions and conservation laws for lossy nonlinear transmission line equation

    Science.gov (United States)

    Tchier, Fairouz; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Inc, Mustafa

    2017-07-01

    In this article, the Lie symmetry and Ricatti-Bernoulli (RB) sub-ODE method are applied to obtain soliton solutions for nonlinear transmission line equation (NLTLs). The NLTLs is defined to be a structure whereby a short-duration pulses known as electrical solitons can be invented and disseminated. We compute conservation laws (Cls) via a non-linear self-adjointness approach. A suitable substitution for NLTLs is found and the obtained substitution makes the NLTLs equation a non-linearly self-adjoint. We establish Cls for NLTLs equation by the new Cls theorem presented by Ibragimov. We obtain trigonometric, algebraic and soliton solutions. The obtained solutions can be useful for describing the concentrations of transmission lines problems, for NLTLs. The parameters of the transmission line play a significant role in managing the original form of the soliton.

  16. How many soliton solutions are there in the Landau-Lifshits equation for uniaxial ferromagnetic?

    International Nuclear Information System (INIS)

    Ostrovskaya, Natalia

    2010-01-01

    The well-known Akhiezer-Borovik soliton is only the simplest solution in the set of solitons in this problem. In our work the general traveling-wave solution of the Landau-Lifshits equation was found in the form of elliptic integral of the first kind avoiding the inverse scattering method. The solution contains four independent constants of integration, two of which are just shearing ones, and the additional parameter - the wave velocity. The bifurcation manifold for the solution in three-dimensional bifurcation space consists of five surfaces. On four of them there are the regions, where the soliton solutions of the classical localized form do exist. For the parameter combinations out of these surfaces there are the regions of periodic cnoidal solutions and the regions without any real solutions, but with complex ones only.

  17. Optical soliton solutions for two coupled nonlinear Schroedinger systems via Darboux transformation

    International Nuclear Information System (INIS)

    Zhang Haiqiang; Li Juan; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo

    2007-01-01

    In nonlinear optical fibers, the vector solitons can be governed by the systems of coupled nonlinear Schroedinger from polarized optical waves in an isotropic medium. Based on the Ablowitz-Kaup-Newell-Segur technology, the Darboux transformation method is successfully applied to two coupled nonlinear Schroedinger systems. With the help of symbolic computation, the bright vector one- and two-soliton solutions including one-peak and two-peak solitons are further constructed via the iterative algorithm of Darboux transformation. Through the figures for several sample solutions, the stable propagation and elastic collisions for these kinds of bright vector solitons are discussed and the possible applications are pointed out in optical communications and relevant optical experiments.In addition, the conserved quantities of such two systems, i.e., the energy, momentum and Hamiltonian, are also presented

  18. Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

    Directory of Open Access Journals (Sweden)

    Golovaty Yuriy

    2017-04-01

    Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.

  19. New soliton solutions of the system of equations for the ion sound and Langmuir waves

    Directory of Open Access Journals (Sweden)

    Seyma Tuluce Demiray

    2016-11-01

    Full Text Available This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM, which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

  20. Double Wronskian Solution and Soliton Properties of the Nonisospectral BKP Equation

    Science.gov (United States)

    Wang, Deng-Shan; Li, Xiang-Gui; Chan, C. K.; Zhou, Jian

    2016-03-01

    Based on the Wronskian technique and Lax pair, double Wronskian solution of the nonisospectral BKP equation is presented explicitly. The speed and dynamical influence of the one soliton are discussed. Soliton resonances of two soliton are shown by means of density distributions. Soliton properties are also investigated in the inhomogeneous media. Supported by the Research Committee of The Hong Kong Polytechnic University under Grant No. G-YM37, the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics under Grant No. 1-ZVA8, National Natural Science Foundation of China under Grant Nos. 11271362 and 11375030, Beijing Natural Science Fund Project and Beijing City Board of Education Science and Technology Key Project under Grant No. KZ201511232034, Beijing Natural Science Foundation under Grant No. 1153004, Beijing Nova Program No. Z131109000413029, and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

  1. Classical solutions in quantum field theory solitons and instantons in high energy physics

    CERN Document Server

    Weinberg, Erick J

    2012-01-01

    Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on ...

  2. Solitons and periodic solutions to a couple of fractional nonlinear ...

    Indian Academy of Sciences (India)

    2014-02-26

    Feb 26, 2014 ... Home; Journals; Pramana – Journal of Physics; Volume 82; Issue 3 ... First integral method; solitons; foam drainage equation; Klein–Gordon equation. ... East of Guilan, University of Guilan, Rudsar, Iran; Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran ...

  3. Soliton solutions for a quasilinear Schrödinger equation via Morse ...

    Indian Academy of Sciences (India)

    weak solutions to a class of quasilinear Schrödinger equation of the form. − pu − p. 2p−1 u p(u. 2. ) = f (x, u) in a bounded smooth domain. ⊂ RN with Dirichlet boundary condition. Keywords. Quasilinear Schrödinger equation; soliton solution; critical point; Morse theory; local linking. 1991 Mathematics Subject Classification.

  4. Existence of positive weak solutions for a class of singular elliptic equations

    Directory of Open Access Journals (Sweden)

    Li Xia

    2011-08-01

    Full Text Available In this note, we are concerned with positive solutions for a class of singular elliptic equations. Under some conditions, we obtain weak solutions for the equations by elliptic regularization method and sub-super solution method.

  5. Soliton Perturbations, Revisited.

    Science.gov (United States)

    Herman, Russell Leland

    Starting with an 'integrable' nonlinear evolution equation, we are investigating perturbations about a one soliton solution, through the inversion of a linear equation for the first order correction. This differs from the methods based on the perturbation of certain 'scattering data', as the proposed method takes place in coordinate space, and not spectral space. The method is tested on several perturbed Korteweg -DeVries equations. The damped KdV equation is studied in detail, resulting in the resolution of the controversy over the shift in the center of the soliton in favor of the results of Karpman and Maslov. Using a finite difference scheme, a numerically induced shift in the damped soliton's position is predicted through the use of perturbation theory. We extend the results of Ott and Sudan for other damped KdV equations, giving expressions for the shift in soliton position and the asymptotic form of the first order correction to the solution. Next we investigate Menyuk's case of a solution consisting of a soliton plus arbitrary initial radiation, which is subject to a Hamiltonian perturbation; and we show that the radiation must start out small. After these preliminary investigations, we turn to the stochastic KdV equation with external Gaussian white noise, zeta(x,t). For the cases of damping and no damping, the averaged soliton asymptotically becomes a Gaussian wave packet, which decays and broadens according to the same power laws as found by Wadati and Akutsu for the noise zeta(t). Next, we investigate the propagation of a modulated KP soliton and compare our results to the work of Chang. We find that singular perturbation theory cannot explain the evolution of this profile, but we can obtain good qualitative results from the solution of the Cauchy problem for the linearized KP equation. The modulations travel away from the soliton peak and decay in time, leaving a stable planar soliton behind. Finally, we discuss the application of the method to the

  6. Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method

    International Nuclear Information System (INIS)

    Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.

    2007-01-01

    In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple

  7. Infinite derivative gravity : non-singular cosmology & blackhole solutions

    NARCIS (Netherlands)

    Mazumdar, Anupam

    2017-01-01

    Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and

  8. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Directory of Open Access Journals (Sweden)

    Aly R. Seadawy

    2018-03-01

    Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave

  9. Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems

    Directory of Open Access Journals (Sweden)

    Gernot Pulverer

    2010-01-01

    Full Text Available In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u, u′(0=0, βu′(1+αu(1=A, where λ is a nonnegative parameter, β≥0, α>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [0,ρ]⊂[0,1, the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u=1/u and for some model problems from the class of singular differential equations (ϕ(u′′+f(t,u′=λg(t,u,u′ discussed in Agarwal et al. (2007. For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.

  10. Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

    Science.gov (United States)

    Pan, Supriya

    2018-01-01

    Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

  11. Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

    Science.gov (United States)

    Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

    2017-07-01

    The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

  12. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    Science.gov (United States)

    Seadawy, Aly R.; Manafian, Jalil

    2018-03-01

    This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

  13. Symmetry reduction and new non-traveling wave solutions of (2 + 1)-dimensional breaking soliton equation

    Science.gov (United States)

    Da-Quan, Xian

    2010-08-01

    In this paper, the new idea of a combination of Lie group method and homoclinic test technique is first proposed to seek non-traveling wave solutions of (2 + 1)-dimensional breaking soliton equation. The system is reduced to some (1 + 1)-dimensional nonlinear equations by applying the Lie group method and solves reduced equation with homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions of similar systems can be obtained.

  14. The Hopf–Cole transformation, topological solitons and multiple fusion solutions for the n-dimensional Burgers system

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yang, E-mail: yayangchen@umac.mo [Department of Mathematics, University of Macau, Macau (China); Fan, Engui, E-mail: faneg@fudan.edu.cn [School of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433 (China); Yuen, Manwai, E-mail: nevetsyuen@hotmail.com [Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories (Hong Kong)

    2016-01-08

    We show that, under an irrotational condition, there exists an n-dimensional Hopf–Cole transformation between the n-dimensional Burgers system and an n-dimensional heat equation. Further, as application of the Hopf–Cole transformation, two kinds of physically interesting exact solutions for the n-dimensional Burgers equations are found. In the first kind of solutions, the velocity fields are topological solitons. In the second kind of solutions, velocity fields are all multiple fusion soliton solutions. - Highlights: • Find an irrotational condition to linearize n-dimensional Burgers system. • Generalize classical Hopf–Cole transformation to n-dimensional Burgers system. • Present topological solitons and multiple fusion soliton solutions.

  15. Travelling wave solutions for a singularly perturbed Burgers–KdV ...

    Indian Academy of Sciences (India)

    Abstract. This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, ...

  16. Travelling wave solutions for a singularly perturbed Burgers–KdV ...

    Indian Academy of Sciences (India)

    This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

  17. Bäcklund transformation and soliton solutions in terms of the Wronskian for the Kadomtsev-Petviashvili-based system in fluid dynamics

    Science.gov (United States)

    Du, Zhong; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Wu, Xiao-Yu

    2018-04-01

    In this paper, investigation is made on a Kadomtsev-Petviashvili-based system, which can be seen in fluid dynamics, biology and plasma physics. Based on the Hirota method, bilinear form and Bäcklund transformation (BT) are derived. N-soliton solutions in terms of the Wronskian are constructed, and it can be verified that the N-soliton solutions in terms of the Wronskian satisfy the bilinear form and Bäcklund transformation. Through the N-soliton solutions in terms of the Wronskian, we graphically obtain the kink-dark-like solitons and parallel solitons, which keep their shapes and velocities unchanged during the propagation.

  18. Noncommutative solitons

    International Nuclear Information System (INIS)

    Gopakumar, R.

    2002-01-01

    Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect

  19. Generalized dark-bright vector soliton solution to the mixed coupled nonlinear Schrödinger equations.

    Science.gov (United States)

    Manikandan, N; Radhakrishnan, R; Aravinthan, K

    2014-08-01

    We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.

  20. Homogeneous Solutions of Stationary Navier-Stokes Equations with Isolated Singularities on the Unit Sphere. I. One Singularity

    Science.gov (United States)

    Li, Li; Li, YanYan; Yan, Xukai

    2018-03-01

    We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (-1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (-1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.

  1. Extended Soliton Solutions in an Effective Action for SU(2 Yang-Mills Theory

    Directory of Open Access Journals (Sweden)

    Nobuyuki Sawado

    2006-01-01

    Full Text Available The Skyrme-Faddeev-Niemi (SFN model which is an O(3 σ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2 Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.

  2. A set of exact two soliton wave solutions to Einstein field equations

    International Nuclear Information System (INIS)

    Wang Youtang; He Zhixian

    1991-09-01

    A set of exact solutions of Einstein equations in vacuum is obtained. Taking this set of solutions as seed solutions and making use of the Belinsky-Zakharov generation technique a set of generated solutions is constructed. Both set of exact solutions and a set of generated solutions describe two solition waves, which propagate in opposite directions and collide with each other, and then recover their original shapes. The singularities of the two set of solutions are analyzed. The relationship between our solutions and other solutions is also discussed. (author). 11 refs, 4 figs

  3. Review of singular potential integrals for method of moments solutions of surface integral equations

    Directory of Open Access Journals (Sweden)

    A. Tzoulis

    2004-01-01

    Full Text Available Accurate evaluation of singular potential integrals is essential for successful method of moments (MoM solutions of surface integral equations. In mixed potential formulations for metallic and dielectric scatterers, kernels with 1/R and r1/R singularities must be considered. Several techniques for the treatment of these singularities will be reviewed. The most common approach solves the MoM source integrals analytically for specific observation points, thus regularizing the integral. However, in the case of r1/R a logarithmic singularity remains for which numerical evaluation of the testing integral is still difficult. A recently by Yl¨a-Oijala and Taskinen proposed remedy to this issue is discussed and evaluated within a hybrid finite element – boundary integral technique. Convergence results for the MoM coupling integrals are presented where also higher-order singularity extraction is considered.

  4. Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions

    Directory of Open Access Journals (Sweden)

    Yakup Yıldırım

    Full Text Available In this study, we perform the extended Kudryashov method to nonlinear Schrödinger equation (NLSE with spatio-temporal dispersion that arises in a propagation of light in nonlinear optical fibers, planar waveguides, Bose–Einstein condensate theory. Four types of nonlinearity – Kerr law, power law, parabolic law and dual-power law – are being considered for the model. By using this scheme, the topological, singular soliton and rational solutions are obtained. In addition, some graphical simulations of solutions are provided.It is demonstrated that the proposed algorithm is effective and can be handled for many other nonlinear complex differential equations. Keywords: Solitons, Nonlinear Schrödinger equation with spatio-temporal dispersion, Extended Kudryashov’s method

  5. Multi-soliton solutions of the Einstein equation and the Tomimatsu-Sato metric

    International Nuclear Information System (INIS)

    Tomimatsu, Akira; Sato, Humitaka.

    1982-01-01

    We present a new recognition about the Tomimatsu-Sato metric through reviewing the recent study of the stationary and axially symmetric Einstein field equation. We describe some powerful methods of solving the Einstein equation; the Baecklund transformation, the inverse scattering method and any other. These methods derive the so-called multi-soliton solution, which represents the Kerr-NUT metric or a non-linear superposition of several Kerr-NUT metrics aligned along their common rotational axis. The Tomimatsu-Sato metric of delta = N is constructed via a limiting process that the N Kerr metrics with the same mass and angular momentum approach mutually towards their complete overlapping. We investigate the space-time properties of the multi-soliton metric, by taking the two Kerr case as a typical example. (author)

  6. Details of the general numerical solutions of the Friedberg-Lee soliton model for ground and exited states

    International Nuclear Information System (INIS)

    Koeppel, T.; Harvey, M.

    1984-06-01

    A new numerical method is applied to solving the equations of motion of the Friedberg-Lee Soliton model for both ground and spherically symmetric excited states. General results have been obtained over a wide range of parameters. Critical coupling constants and critical particle numbers have been determined below which soliton solutions cease to exist. The static properties of the proton are considered to show that as presently formulated the model fails to fit all experimental data for any set of parameters

  7. Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions

    Science.gov (United States)

    Ijjas, Anna

    2018-02-01

    In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein's general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition violating stage. Similar considerations apply to galilean genesis scenarios.

  8. The mechanics of delamination in fiber-reinforced composite materials. I - Stress singularities and solution structure

    Science.gov (United States)

    Wang, S. S.; Choi, I.

    1983-01-01

    The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be different from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites. Previously announced in STAR as N84-13221

  9. Existence and regularity of weak solutions for singular elliptic problems

    Directory of Open Access Journals (Sweden)

    Brahim Bougherara

    2015-11-01

    Full Text Available In this article we study the semilinear singular elliptic problem $$\\displaylines{ -\\Delta u = \\frac{p(x}{u^{\\alpha}}\\quad \\text{in } \\Omega \\cr u = 0\\quad \\text{on } \\partial\\Omega,\\quad u>0 \\text{ in } \\Omega, }$$ where $\\Omega$ is a regular bounded domain of $\\mathbb R^{N}$, $\\alpha\\in\\mathbb R$, $p\\in C(\\Omega$ which behaves as $d(x^{-\\beta}$ as $x\\to\\partial\\Omega$ with $d$ the distance function up to the boundary and $0\\leq \\beta 1$.

  10. Constructing Soliton and Kink Solutions of PDE Models in Transport and Biology

    Directory of Open Access Journals (Sweden)

    Vsevolod A. Vladimirov

    2006-06-01

    Full Text Available We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these wave patterns is carried out by means of our modification of the direct algebraic balance method. In the case when the analytical description fails, we propose to approximate invariant travelling wave solutions by means of an infinite series of exponential functions. The effectiveness of the method of approximation is demonstrated on a hyperbolic modification of Burgers equation.

  11. Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

    Directory of Open Access Journals (Sweden)

    Burkhan T. Kalimbetov

    2012-01-01

    Full Text Available The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.

  12. Cosmological solutions and finite time singularities in Finslerian geometry

    Science.gov (United States)

    Paul, Nupur; de, S. S.; Rahaman, Farook

    2018-03-01

    We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.

  13. Optical solitons with DWDM technology and four-wave mixing

    Science.gov (United States)

    Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, Milivoj

    2017-07-01

    This paper obtains bright and singular optical soliton solutions to DWDM system in presence of four-wave mixing. The extended trial function scheme is adopted. The two types of nonlinear media studied are Kerr law and parabolic law. There are other types of waves that appears as a byproduct to this scheme.

  14. Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions.

    Science.gov (United States)

    Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit

    2015-02-01

    We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.

  15. Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

    Science.gov (United States)

    Liu, Nan; Wen, Xiao-Yong

    2018-03-01

    Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

  16. Smoothness and numerical solution of linear integral equations of the second type with weakly singular kernels

    International Nuclear Information System (INIS)

    Bechlars, J.

    1978-12-01

    1) Integrable (L 1 ) singularities, occuring on the boundary or along the diagonal direction, and jumps along the diagonal direction do not disturb the compactness of otherwise continuous integral operator kernels. So the theory of compact operators can be applied for solving the integral equation. 2) Provided the regular parts of the kernel are sufficiently differentiable, the continuous differentiability (Cn) of the right hand side is transposed to the solution, if the kernel has no singularities or no singularities on the boundary and no jump. In the case of singularities in connection with a jump examples show, that this result is not valid in general. Therefore a second definition of smoothness has been introduced (Csup((n,α)) : continuous differentiability in the interior and 'limitation of derivatives') which can be applied in such cases and on the other side shows satisfactory error behaviour during interpolation and includes singularities from logarithms and negative powers. Provided diagonal singularities or singularities on the boundary can be asigned to Csup((n+1,α-1)) (0 2 also Csup((2,α)) (0 -2 ). This is confirmed by numerical examples. (orig./HSI) [de

  17. Periodic solutions to singular second order differential equations: the repulsive case

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Torres, P.J.; Zamora, M.

    2012-01-01

    Roč. 39, č. 2 (2012), s. 199-220 ISSN 1230-3429 Institutional support: RVO:67985840 Keywords : singular nonlinear boundary value problem * positive solutions * periodic solutions Subject RIV: BA - General Mathematics Impact factor: 1.099, year: 2012

  18. Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

    Directory of Open Access Journals (Sweden)

    Zonghu Xiu

    2012-01-01

    Full Text Available We consider the existence of multiple solutions of the singular elliptic problem , as , where , , , , , , . By the variational method and the theory of genus, we prove that the above-mentioned problem has infinitely many solutions when some conditions are satisfied.

  19. Topological and non-topological soliton solutions to some time ...

    Indian Academy of Sciences (India)

    While there are other relativistic wave equations, Klein–Gordon equation has been the most frequently studied equation for describing particle dynamics in quantum field theory [4,5]. The construction of exact and analytical travelling wave solutions of nonlinear fractional partial differential equations is one of the most impor-.

  20. Topological and non-topological soliton solutions to some time ...

    Indian Academy of Sciences (India)

    This paper investigates, for the first time, the applicability and effectiveness of He's semi-inverse variational principle method and the ansatz method on systems of nonlinear fractional partial differential equations. He's semi-inverse variational principle method and the ansatz method are used to construct exact solutions of ...

  1. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  2. Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources

    Directory of Open Access Journals (Sweden)

    Ida de Bonis

    2017-09-01

    Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

  3. Soliton solutions of cubic-quintic nonlinear Schrödinger equation with combined time-dependent magnetic-optical potentials

    Science.gov (United States)

    Li, H. M.; Zhao, J. Q.; You, L. Y.

    2015-10-01

    We investigate the explicit matter-wave soliton solutions of the cubic-quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. With a systematic way, we construct some integrable systems with localized cubic-quintic nonlinearities and an infinite number of potentials, including optical lattice potential and combined time-dependent magnetic-optical potentials in the form of linear-lattice, harmonic-lattice and harmonic-linear-lattice ones. Also, corresponding analytical localized soliton solutions in terms of Mathieu and elliptic functions are studied, such as snake solitons, moving breathing solitons and oscillating solitons. Finally, some stable solitons are found by means of the stability analysis of the exact solutions with the split-step Fourier transform method.

  4. On the stability of soliton solution in NLS-type general field model

    International Nuclear Information System (INIS)

    Chakrabarti, S.; Nayyar, A.H.

    1982-08-01

    A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)

  5. Non linear photons: a non singular cosmological solution

    International Nuclear Information System (INIS)

    Alves, G.A.

    1986-01-01

    The validity of equivalence principle as principle of minimum coupling between field interactions, is discussed. The non minimum coupling between vector field and gravitational field, and some consequences of this coupling are analysed. Starting from spherical symmetry metric, the coupled field equations, obtaining exact solutions and interpreting these solutions, are solved. (M.C.K.) [pt

  6. Fully stable cosmological solutions with a non-singular classical bounce

    Science.gov (United States)

    Ijjas, Anna; Steinhardt, Paul J.

    2017-01-01

    We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L4 Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.

  7. Orbits 2nd order singularity-free solutions

    CERN Document Server

    Xu, Guochang

    2014-01-01

    In its 2nd edition, this book covers the theory of satellite orbits, derives the complete solutions of orbital disturbances, describes the algorithms of orbits determination and the applications of the theory to the phenomenon of physical satellite formation.

  8. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    , is used to solve this equation. This method is able to obtain rapidly convergent successive approximations of exact solution without any restrictive approximations or the transformations that may change the physical behaviour of the problem.

  9. Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma

    Energy Technology Data Exchange (ETDEWEB)

    Batool, Nazia; Jahangir, R. [Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan); Masood, W. [National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan); COMSATS Institute of Information Technology, Islamabad (Pakistan); Siddiq, M. [National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan)

    2016-08-15

    In the present investigation, cylindrical Kadomstev-Petviashvili (CKP) equation is derived in pair-ion-electron plasmas to study the propagation and interaction of two solitons. Using a novel gauge transformation, two soliton solutions of CKP equation are found analytically by using Hirota's method and to the best of our knowledge have been used in plasma physics for the first time. Interestingly, it is observed that unlike the planar Kadomstev-Petviashvili (KP) equation, the CKP equation admits horseshoe-like solitary structures. Another non-trivial feature of CKP solitary solution is that the interaction parameter gets modified by the plasma parameters contrary to the one obtained for Korteweg–de Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.

  10. Ponderable soliton stars

    Science.gov (United States)

    Chiu, Hong-Yee

    1990-01-01

    The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.

  11. Multiple solutions to some singular nonlinear Schrodinger equations

    Directory of Open Access Journals (Sweden)

    Monica Lazzo

    2001-01-01

    Full Text Available We consider the equation $$ - h^2 Delta u + V_varepsilon(x u = |u|^{p-2} u $$ which arises in the study of standing waves of a nonlinear Schrodinger equation. We allow the potential $V_varepsilon$ to be unbounded below and prove existence and multiplicity results for positive solutions.

  12. Uniqueness of singular solution of semilinear elliptic equation

    Indian Academy of Sciences (India)

    1Institute of Contemporary Mathematics; 2School of Mathematics and. Information Science, Henan University, Kaifeng 475004, People's Republic of China. E-mail: laibaishun@henu.edu.cn. MS received 13 December 2009; revised 19 May 2010. Abstract. In this paper, we study asymptotic behavior of solution near 0 for a ...

  13. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing

    2009-01-01

    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  14. Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2018-01-01

    Roč. 70, č. 1 (2018), s. 173-190 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : indefinite singularity * periodic solution * Kepler problem on S^1 Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.963, year: 2016 https://cms.math.ca/10.4153/CJM-2016-050-1

  15. Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

    Science.gov (United States)

    Cortissoz, Jean C.; Montero, Julio A.

    2018-03-01

    In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Navier-Stokes equations, and we also present an elementary proof for a lower bound on blow-up rate of the Sobolev norms of possible singular solutions to the Euler equations when s>5/2.

  16. Existence and uniqueness of a periodic solution to an indefinite attractive singular equation

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2016-01-01

    Roč. 195, č. 3 (2016), s. 995-1009 ISSN 0373-3114 Institutional support: RVO:67985840 Keywords : singular differential equation * periodic solution * uniqueness Subject RIV: BA - General Mathematics Impact factor: 0.864, year: 2016 http://link.springer.com/article/10.1007%2Fs10231-015-0501-3

  17. On solutions of neutral stochastic delay Volterra equations with singular kernels

    Directory of Open Access Journals (Sweden)

    Xiaotai Wu

    2012-08-01

    Full Text Available In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

  18. Holder regularity for signed solutions to singular porous medium type equations

    Directory of Open Access Journals (Sweden)

    Simona Puglisi

    2012-11-01

    Full Text Available We prove Holder regularity for bounded signed solution to singular porous medium type equations, whose prototype is $$ u_t-hbox{div}m|u|^{m-1}Du=0quadhbox{weakly in }E_T, $$ with $min(0,1$.

  19. Periodic solutions to the Liénard type equations with phase attractive singularities

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    -, 6 March (2013), s. 47 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : Rayleigh-Plesset equation * singular equation * periodic solution Subject RIV: BA - General Mathematics Impact factor: 0.836, year: 2013 http://www.boundaryvalueproblems.com/content/2013/1/47

  20. Bright and dark soliton solutions for some nonlinear fractional differential equations

    Science.gov (United States)

    Ozkan, Guner; Ahmet, Bekir

    2016-03-01

    In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona-Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann-Liouville sense.

  1. Existence of positive solutions and eigenvalues intervals for nonlinear Sturm Liouville problems with a singular interface

    Directory of Open Access Journals (Sweden)

    D. K. K. Vamsi

    2012-03-01

    Full Text Available In this article, we define the Green's matrix for a nonlinear Sturm Liouville problem associated with a pair of dynamic equations on time scales with a singularity at the point of interface. Then using iterative techniques, we obtain eigenvalue intervals for which there exist positive solutions. Then we present iterative schemes for approximating the solutions, and discus an example that illustrates the the results obtained.

  2. Existence of Positive Solutions to Singular -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

    Directory of Open Access Journals (Sweden)

    Qiying Wei

    2009-01-01

    Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.

  3. General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

    Science.gov (United States)

    Kanna, T; Sakkaravarthi, K; Tamilselvan, K

    2013-12-01

    We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction

  4. Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations.

    Science.gov (United States)

    Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman

    2015-04-01

    The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.

  5. Constructing and analysis of soliton-like solutions of (1 + 1), (2 + 1), (3 + 1)-dimensional Schrodinger equations with the third power nonlinearity law

    International Nuclear Information System (INIS)

    Zhestkov, S.V.; Romanenko, A.A.

    2009-01-01

    The problem of existence of soliton-like solutions of (1+1), (2+1), (3+1)-dimensional Schrodinger equations with the third power nonlinearity law is investigated. The numerical-analytical method of constructing solitons is developed. (authors)

  6. New class of inhomogeneous cosmological perfect-fluid solutions without big-bang singularity

    Energy Technology Data Exchange (ETDEWEB)

    Senovilla, J.M.M. (Grupo de Fisica Teorica, Departamento de Fisica, Ingenieria y Radiologia Medica, Facultad de Ciencias, Universidad de Salamanca, 37008 Salmanaca (Spain))

    1990-05-07

    A new class of exact solutions to Einstein's field equations with a perfect-fluid source is presented. The solutions describe spatially inhomogeneous cosmological models and have a realistic equation of state {ital p}={rho}/3. The properties of the solutions are discussed. The most remarkable feature is the absence of an initial singularity, the curvature and matter invariants being regular and smooth everywhere. We also present an alternative interpretation of the solution as a globally regular cylindrically symmetric space-time.

  7. An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

    Science.gov (United States)

    Drivas, Theodore D.; Eyink, Gregory L.

    2017-12-01

    We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

  8. Compactons versus solitons

    Indian Academy of Sciences (India)

    generalized Korteweg–de Vries equations admit genuine soliton solutions besides com- pacton 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 ...

  9. Abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system

    Science.gov (United States)

    Wazwaz, Abdul-Majid

    2012-06-01

    In this work, we explore a variety of solitary wave ansatze and periodic wave ansatze to some nonlinear equations. Three complex systems of nonlinear equations that appear in mathematical physics are investigated. We derive abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system. The results obtained show that these three coupled equations exhibit the richness of explicit solutions: solitons, periodic and rational wave solutions.

  10. The nonlinear Schrödinger equation singular solutions and optical collapse

    CERN Document Server

    Fibich, Gadi

    2015-01-01

    This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fib...

  11. Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order -Point Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Lv Xuezhe

    2010-01-01

    Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.

  12. Singular Solutions to a (3 + 1-D Protter-Morawetz Problem for Keldysh-Type Equations

    Directory of Open Access Journals (Sweden)

    Nedyu Popivanov

    2017-01-01

    Full Text Available We study a boundary value problem for (3 + 1-D weakly hyperbolic equations of Keldysh type (problem PK. The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations which, in part, are closely connected with transonic fluid dynamics. We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. It is known that it may have a strong power-type singularity at one boundary point even for very smooth right-hand sides of the equation. In the present paper we study the asymptotic behavior of the generalized solutions of problem PK at the singular point. There are given orthogonality conditions on the right-hand side of the equation, which are necessary and sufficient for the existence of a generalized solution with fixed order of singularity.

  13. Dark Soliton Solutions of Space-Time Fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili Equations

    Science.gov (United States)

    Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet

    2017-02-01

    Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

  14. A combined variational-topological approach for dispersion-managed solitons in optical fibers

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Torres, P.J.

    2011-01-01

    Roč. 62, č. 2 (2011), s. 245-266 ISSN 0044-2275 Institutional research plan: CEZ:AV0Z10190503 Keywords : optical soliton * Schrödinger equation * singular equation * periodic solution * upper and lower function Subject RIV: BA - General Mathematics Impact factor: 0.951, year: 2011 http://www.springerlink.com/content/y1534p553r530451/

  15. Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity

    Directory of Open Access Journals (Sweden)

    Alberto Lastra

    2018-02-01

    Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.

  16. Singularities in K-space and multi-brane solutions in cubic string field theory

    Science.gov (United States)

    Hata, Hiroyuki; Kojita, Toshiko

    2013-02-01

    In a previous paper [arXiv:1111.2389], we studied the multi-brane solutions in cubic string field theory by focusing on the topological nature of the "winding number" {N} which counts the number of branes. We found that {N} can be non-trivial owing to the singularity from the zero-eigenvalue of K of the KBc algebra, and that solutions carrying integer {N} and satisfying the EOM in the strong sense is possible only for {N} = 0 , ±1. In this paper, we extend the construction of multi-brane solutions to | {N} | ≥ 2. The solutions with N = ±2ismadepossiblebythefactthatthecorrelatorisinvariantunderatransformation exchanging K with 1 /K and hence K = ∞ eigenvalue plays the same role as K = 0. We further propose a method of constructing solutions with | {N} | ≥ 3 by expressing the eigenvalue space of K as a sum of intervals where the construction for | {N} | ≤ 2 is applicable.

  17. Two-Dimensional Spatial Solitons in Nematic Liquid Crystals

    International Nuclear Information System (INIS)

    Zhong Weiping; Xie Ruihua; Goong Chen; Belic, Milivoj; Yang Zhengping

    2009-01-01

    We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Gaussian solitons, radially symmetric solitons, multipole solitons, and soliton vortices.

  18. Symbolic computation on the multi-soliton-like solutions of the cylindrical Kadomtsev-Petviashvili equation from dusty plasmas

    International Nuclear Information System (INIS)

    Li Juan; Zhang Haiqiang; Xu Tao; Zhang Yaxing; Hu Wei; Tian Bo

    2007-01-01

    Considering the transverse perturbation and axially non-planar geometry, the cylindrical Kadomtsev-Petviashvili (KP) equation is investigated in this paper, which can describe the propagation of dust-acoustic waves in the dusty plasma with two-temperature ions. Through imposing the decomposition method, such a (2+1)-dimensional equation is decomposed into two variable-coefficient (1+1)-dimensional integrable equations of the same hierarchy. Furthermore, three kinds of Darboux transformations (DTs) for these two (1+1)-dimensional equations are constructed. Via the three DTs obtained, the multi-soliton-like solutions of the cylindrical KP equation are explicitly presented. Especially, the one- and two-parabola-soliton solutions are discussed by several figures and some effects resulting from the physical parameters in the dusty plasma and transverse perturbation are also shown

  19. Integrable Abelian vortex-like solitons

    Directory of Open Access Journals (Sweden)

    Felipe Contatto

    2017-05-01

    Full Text Available We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.

  20. Integrable Abelian vortex-like solitons

    Energy Technology Data Exchange (ETDEWEB)

    Contatto, Felipe, E-mail: felipe.contatto@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020 (Brazil)

    2017-05-10

    We propose a modified version of the Ginzburg–Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a given class of models. Explicit solutions are determined in terms of the third Painlevé transcendents, allowing us to calculate physical quantities such as the vortex number and the vortex strength. These solutions can be interpreted as the usual Abelian-Higgs vortices on surfaces of non-constant curvature with conical singularity.

  1. Breaking soliton equations and negative-order breaking soliton ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 87; Issue 5. Breaking soliton ... We use the simplified Hirota's method to obtain multiple soliton solutions for each developed breaking soliton equation. We also develop ... WAZWAZ1. Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA ...

  2. Existence of localizing solutions in plasticity via the geometric singular perturbation theory

    KAUST Repository

    Lee, Min-Gi

    2017-01-31

    Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to reveal the onset of localization into shear bands using a simple model from viscoplasticity. We exploit the properties of scale invariance of the model to construct a family of self-similar focusing solutions that capture the nonlinear mechanism of shear band formation. The key step is to desingularize a reduced system of singular ordinary differential equations and reduce the problem into the construction of a heteroclinic orbit for an autonomous system of three first-order equations. The associated dynamical system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré--Bendixson theorem to construct a heteroclinic orbit.

  3. Oscillating solitons in nonlinear optics

    Indian Academy of Sciences (India)

    Abstract. 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 ...

  4. Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Winfried Auzinger

    2006-01-01

    Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

  5. Ground state solutions for Choquard type equations with a singular potential

    Directory of Open Access Journals (Sweden)

    Tao Wang

    2017-02-01

    Full Text Available This article concerns the Choquard type equation $$ -\\Delta u+V(xu=\\Big(\\int_{\\mathbb{R}^N}\\frac{|u(y|^p}{|x-y|^{N-\\alpha}}dy\\Big |u|^{p-2}u,\\quad x\\in \\mathbb{R}^N, $$ where $N\\geq3$, $\\alpha\\in ((N-4_+,N$, $2\\leq p <(N+\\alpha/(N-2$ and V(x is a possibly singular potential and may be unbounded below. Applying a variant of the Lions' concentration-compactness principle, we prove the existence of ground state solution of the above equations.

  6. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

    Directory of Open Access Journals (Sweden)

    Ziheng Zhang

    2014-01-01

    Full Text Available We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS where -∞singularity at 0≠ξ∈ℝN, and Wuu is the gradient of W at u. The novelty of this paper is that, for the case that N≥3 and (HS is nonautonomous (neither periodic nor almost periodic, we show that (HS possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of W. Different from the cases that (HS is autonomous at≡1 or (HS is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS is nonautonomous and N≥3. Besides the usual conditions on W, we need the assumption that a′t<0 for all t∈ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

  7. Spectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric

    Energy Technology Data Exchange (ETDEWEB)

    Belgiorno, F. [Politecnico di Milano, Dipartimento di Matematica, Milan (Italy); INdAM-GNFM, Rome (Italy); INFN, Milan (Italy); Cacciatori, S.L. [Universita dell' Insubria, Department of Science and High Technology, Como (Italy); INFN, Milan (Italy); Vigano, A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milan (Italy)

    2017-06-15

    Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields φ, ψ, respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behavior for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field ψ, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behavior is analyzed too. (orig.)

  8. Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

    Directory of Open Access Journals (Sweden)

    Jian Wang

    2009-01-01

    Full Text Available We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: (|f′|p−2f′′+βrf′+αf+(fq′=0 satisfying a specific decay rate: lim⁡r→∞rα/βf(r=0 with α:=(p−1/(pq−2p+2 and β:=(q−p+1/(pq−2p+2. Here p>2 and q>p−1. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term ut=(|ux|p−2uxx+(uqx defined on the half line [0,+∞.

  9. Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method

    International Nuclear Information System (INIS)

    Mosna, Ricardo A.

    2006-01-01

    Although it is well known that the Seiberg-Witten equations do not admit nontrivial L 2 solutions in flat space, singular solutions to them have been previously exhibited--either in R 3 or in the dimensionally reduced spaces R 2 and R 1 --which have physical interest. In this work, we employ an extension of the Hopf fibration to obtain an iterative procedure to generate particular singular solutions to the Seiberg-Witten and Freund equations on flat space. Examples of solutions obtained by such method are presented and briefly discussed

  10. The mechanics of delamination in fiber-reinforced composite materials. Part 1: Stress singularities and solution structure

    Science.gov (United States)

    Wang, S. S.; Choi, I.

    1983-01-01

    The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites.

  11. Compactons versus solitons

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 74; Issue 6. Compactons versus solitons ... by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable. ... Centre for Mathematical Science, City University London, Northampton Square, London EC1V 0HB, UK ...

  12. Integrability and soliton solutions for an inhomogeneous generalized fourth-order nonlinear Schrödinger equation describing the inhomogeneous alpha helical proteins and Heisenberg ferromagnetic spin chains

    International Nuclear Information System (INIS)

    Wang, Pan; Tian, Bo; Jiang, Yan; Wang, Yu-Feng

    2013-01-01

    For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β

  13. 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.

  14. Singular solutions for the rigid plastic double slip and rotation model under plane strain

    Science.gov (United States)

    Alexandrov, S.; Lyamina, E.

    2018-02-01

    In the mechanics of granular and other materials the system of equations comprising the rigid plastic double slip and rotation model together with the stress equilibrium equations under plane strain conditions forms a hyperbolic system. Boundary value problems for this system of equations can involve a frictional interface. An envelope of characteristics may coincide with this interface. In this case, the solution is singular. In particular, some components of the strain rate tensor approach infinity in the vicinity of the frictional interface. Such behavior of solutions is in qualitative agreement with experimental data that show that a narrow layer of localized plastic deformation is often generated near frictional interfaces. The present paper deals with asymptotic analysis of the aforementioned system of equations in the vicinity of an envelope of characteristics. It is shown that the shear strain rate and the spin component in a local coordinate system connected to the envelope follow an inverse square root rule in its vicinity.

  15. Holder continuity of bounded weak solutions to generalized parabolic p-Laplacian equations II: singular case

    Directory of Open Access Journals (Sweden)

    Sukjung Hwang

    2015-11-01

    Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1solution is locally Holder continuous with some degree of commonality between degenerate and singular types. By using geometric characters, our proof does not rely on any of alternatives which is based on the size of solutions.

  16. Massive soliton stars

    Science.gov (United States)

    Chiu, Hong-Yee

    1990-01-01

    The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.

  17. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  18. Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber.

    Science.gov (United States)

    Liu, Lei; Tian, Bo; Chai, Han-Peng; Yuan, Yu-Qiang

    2017-03-01

    Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

  19. Multi-soliton and rogue-wave solutions of the higher-order Hirota system for an erbium-doped nonlinear fiber

    Energy Technology Data Exchange (ETDEWEB)

    Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics

    2014-10-15

    The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.

  20. On the Existence and Uniqueness of Rv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

    Directory of Open Access Journals (Sweden)

    V. Rukavishnikov

    2014-01-01

    Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

  1. Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

    Science.gov (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2017-12-01

    In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

  2. Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: Computational results

    Energy Technology Data Exchange (ETDEWEB)

    Trogdon, Thomas, E-mail: trogdon@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 (United States); Deconinck, Bernard [Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195 (United States)

    2014-01-31

    All solutions of the Korteweg–de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi-)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their asymptotic state for large |x| is (quasi-)periodic, but they may contain solitons, with or without dispersive tails. Such scenarios might occur in the case of localized perturbations of previously present sea swell, for instance. Such solutions have been discussed from an analytical point of view only recently. We numerically demonstrate different features of these solutions.

  3. Soliton ratchets

    OpenAIRE

    Salerno, Mario; Quintero, Niurka R.

    2001-01-01

    The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile that couples, through the damping in the system, to the soliton translational mode. Effective soliton transport is achieved when the internal mode and the external force are phase locked. We use as a working model a generalized double sine-Gordon equation. The phenomenon is expected to be valid for generic soliton ...

  4. On the new soliton and optical wave structures to some nonlinear evolution equations

    Science.gov (United States)

    Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet

    2017-11-01

    In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.

  5. Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

    Energy Technology Data Exchange (ETDEWEB)

    Ganguly, A., E-mail: gangulyasish@rediffmail.com, E-mail: aganguly@maths.iitkgp.ernet.in; Das, A., E-mail: amiya620@gmail.com [Department of Mathematics, IIT Kharagpur, Kharagpur, 721302 West Bengal (India)

    2014-11-15

    We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.

  6. Darboux Transformation and Soliton Solutions for a Variable-Coefficient Modified Kortweg-de Vries Model from Fluid Mechanics, Ocean Dynamics, and Plasma Mechanics

    International Nuclear Information System (INIS)

    Gai Xiaoling; Gao Yitian; Meng Dexin; Wang Lei; Sun Zhiyuan; Feng Qian; Wang Mingzhen; Yu Xin; Zhu Shunhui; Lue Xing

    2010-01-01

    This paper is to investigate a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model, which describes some situations from fluid mechanics, ocean dynamics, and plasma mechanics. By the Ablowitz-Kaup-Newell-Segur procedure and symbolic computation, the Lax pair of the vc-MKdV model is derived. Then, based on the aforementioned Lax pair, the Darboux transformation is constructed and a new one-soliton-like solution is obtained as well. Features of the one-soliton-like solution are analyzed and graphically discussed to illustrate the influence of the variable coefficients in the solitonlike propagation. (general)

  7. The Interactions of N-Soliton Solutions for the Generalized (2+1-Dimensional Variable-Coefficient Fifth-Order KdV Equation

    Directory of Open Access Journals (Sweden)

    Xiangrong Wang

    2015-01-01

    Full Text Available A generalized (2+1-dimensional variable-coefficient KdV equation is introduced, which can describe the interaction between a water wave and gravity-capillary waves better than the (1+1-dimensional KdV equation. The N-soliton solutions of the (2+1-dimensional variable-coefficient fifth-order KdV equation are obtained via the Bell-polynomial method. Then the soliton fusion, fission, and the pursuing collision are analyzed depending on the influence of the coefficient eAij; when eAij=0, the soliton fusion and fission will happen; when eAij≠0, the pursuing collision will occur. Moreover, the Bäcklund transformation of the equation is gotten according to the binary Bell-polynomial and the period wave solutions are given by applying the Riemann theta function method.

  8. On the Theory of Solitons of Fluid Pressure and Solute Density in Geologic Porous Media, with Applications to Shale, Clay and Sandstone

    Science.gov (United States)

    Caserta, A.; Kanivetsky, R.; Salusti, E.

    2017-11-01

    We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear "Burgers solitons". We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.

  9. Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

    Directory of Open Access Journals (Sweden)

    Gai Gongqi

    2011-01-01

    Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

  10. Breaking soliton equations and negative-order breaking soliton ...

    Indian Academy of Sciences (India)

    2016-10-06

    Oct 6, 2016 ... as optical fibres, fluid dynamics, plasma physics, ocean engineering, chemical physics etc. are described by nonlinear equations where soliton solutions may appear. Some of these nonlinear evolution equations are integrable which give multiple soliton solutions. The study of integrable equations, that ...

  11. Existence and rigorous asymptotics of the solutions of a class of singularly perturbed delay-differential equations

    Directory of Open Access Journals (Sweden)

    WANG Na

    2016-06-01

    Full Text Available We consider the singularly perturbed delayed systems of Tichonov′s type with fast and slow variables in a fast bimolecular reaction model. By means of the boundary layer function method, sewing connection and the implicit function theorem, we prove the existence of the solutions of our problems near the degenerate solution for a sufficiently small µ and determine its asymptotic behavior in µ. Meanwhile, the asymptotic expression of the systems is also constructed.

  12. Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

    Science.gov (United States)

    Chruściel, Piotr T.; Delay, Erwann; Klinger, Paul

    2018-02-01

    We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein–Maxwell-dilaton-scalar fields-Yang–Mills–Higgs–Chern–Simons-f(R) equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

  13. Helmholtz bright and boundary solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2007-01-01

    We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic nonlinear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently derived Helmholtz bright solitons, for this type of polynomial nonlinearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

  14. Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation

    Science.gov (United States)

    Butuzov, V. F.

    2017-06-01

    We construct and justify asymptotic expansions of solutions of a singularly perturbed elliptic problem with Dirichlet boundary conditions in the case when the corresponding degenerate equation has a triple root. In contrast to the case of a simple root, the expansion is with respect to fractional (non-integral) powers of the small parameter, the boundary-layer variables have another scaling, and the boundary layer has three zones. This gives rise to essential modifications in the algorithm for constructing the boundary functions. Solutions of the elliptic problem are stationary solutions of the corresponding parabolic problem. We prove that such a stationary solution is asymptotically stable and find its global domain of attraction.

  15. What Is the Validity Domain of Einstein’s Equations? Distributional Solutions over Singularities and Topological Links in Geometrodynamics

    Directory of Open Access Journals (Sweden)

    Elias Zafiris

    2016-08-01

    Full Text Available The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions.

  16. Compactons versus solitons

    Indian Academy of Sciences (India)

    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 ...

  17. Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits.

    Science.gov (United States)

    Chowdury, Amdad; Krolikowski, Wieslaw; Akhmediev, N

    2017-10-01

    We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.

  18. Modulational instability: Conservation laws and bright soliton solution of ion-acoustic waves in electron-positron-ion-dust plasmas

    Science.gov (United States)

    EL-Kalaawy, O. H.

    2018-02-01

    We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.

  19. Bilinear Forms and Soliton Solutions for the Reduced Maxwell-Bloch Equations with Variable Coefficients in Nonlinear Optics

    Science.gov (United States)

    Chai, Jun; Tian, Bo; Chai, Han-Peng

    2018-02-01

    Investigation in this paper is given to the reduced Maxwell-Bloch equations with variable coefficients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coefficient-dependent bilinear forms. Then, we construct the one-, two- and N-soliton solutions in analytic forms for them. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, 11471050, the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02

  20. 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.

  1. Soliton model for elementary electric charge

    International Nuclear Information System (INIS)

    Chepilko, N.M.; Kobushkin, A.P.

    1988-01-01

    The existence and topological stability of three-dimensional solitons in Klein-Gordon field electrodynamics are proved. The central-symmetric solution to field equations, which can be interpreted as soliton model of elementary electric charge with zero spin, is constructed. The electrostatic soliton rotation is shown to result in the charge having its own magnetic-dipole field. 9 refs.; 2 figs

  2. Scale symmetry of quantum solitons

    International Nuclear Information System (INIS)

    Chepilko, N.M.; Fujii, K.; Kobushkin, A.P.

    1991-01-01

    A collective-coordinate Lagrangian for a rotating and vibrating quantum soliton in the nonlinear σ-model is shown to possess a symmetry under scale transformation of the chiral field. Using this symmetry an integrodifferential equation for the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is also discussed. At limiting cases (a vibrating, but not rotating soliton; or a rotating, but not vibrating soliton) the integrodifferential ones and the chiral angle becomes independent of the solution of the Schroedinger equation. 7 refs

  3. Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

    Science.gov (United States)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2012-10-01

    A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

  4. Exact solutions of space-time fractional EW and modified EW equations

    International Nuclear Information System (INIS)

    Korkmaz, Alper

    2017-01-01

    The bright soliton solutions and singular solutions are constructed for the space-time fractional EW and the space-time fractional modified EW (MEW) equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform (FCT) and properties of modified Riemann–Liouville derivative. Then, various ansatz method are implemented to construct the solutions for both equations.

  5. Exact solutions of space-time fractional EW and modified EW equations

    Science.gov (United States)

    Korkmaz, Alper

    2017-03-01

    The bright soliton solutions and singular solutions are constructed for space-time fractional EW and modified EW equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. Then, implementation of ansatz method the solutions are constructed.

  6. Exact Solutions of Space-time Fractional EW and modified EW equations

    OpenAIRE

    Korkmaz, Alper

    2016-01-01

    The bright soliton solutions and singular solutions are constructed for space-time fractional EW and modified EW equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative. Then, implementation of ansatz method the solutions are constructed.

  7. Cosmic ray-modified stellar winds. I - Solution topologies and singularities

    Science.gov (United States)

    Ko, C. M.; Webb, G. M.

    1987-01-01

    In the present two-fluid hydrodynamical model for stellar wind flow modification due to its interaction with Galactic cosmic rays, these rays are coupled to the stellar wind by either hydromagnetic wave scattering or background flow irregularity propagation. The background flow is modified by the cosmic rays via their pressure gradient. The system of equations used possesses a line of singularities in (r, u, P sub c)-space, or a two-dimensional hypersurface of singularities in (r, u, P sub c, dP sub c/dr)-space, where r, u, and P sub c are respectively the radial distance from the star, the radial wind flow speed, and the cosmic ray pressure. The singular points may be nodes, foci, or saddle points.

  8. Solitonic fullerene structures in light atomic nuclei.

    Science.gov (United States)

    Battye, R A; Sutcliffe, P M

    2001-04-30

    The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically, using two different minimization algorithms, minimum energy configurations for up to 22 solitons. We find, remarkably, that the solutions for seven or more solitons have nucleon density isosurfaces in the form of polyhedra made of hexagons and pentagons. Precisely these structures arise, though at the much larger molecular scale, in the chemistry of carbon shells, where they are known as fullerenes.

  9. Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

    Science.gov (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2018-01-01

    In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

  10. One- and two-channel Kondo model with logarithmic Van Hove singularity: A numerical renormalization group solution

    Science.gov (United States)

    Zhuravlev, A. K.; Anokhin, A. O.; Irkhin, V. Yu.

    2018-02-01

    Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s-d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.

  11. Asymptotically AdS spacetimes with a timelike Kasner singularity

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)

    2016-07-21

    Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.

  12. Compactons versus solitons

    Indian Academy of Sciences (India)

    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 ... Compactons; PT -symmetry; KdV equation; Painlevé test. .... Cooper et al [25] found that in the generalized KdV equation, i.e. m = 2, a necessary.

  13. Implementation of the HNS Convention in the LNG Industry: Singularities, Stakes, Issues and GIIGNL Proposed Solutions

    International Nuclear Information System (INIS)

    2008-01-01

    The International Group of Liquefied Natural Gas Importers (GIIGNL) is a non-profit organization founded in December of 1971. It is composed of 56 member companies from 18 different countries across the world and involved in the importation of Liquefied Natural Gas. The main objective of the GIIGNL is to promote the development of activities related to LNG: purchasing, importing, processing, transportation, handling, re-gasification and various uses of LNG. For this purpose, the GIIGNL is particularly involved in promoting the state-of-the art technology in the LNG industry, in communicating about the economic fundamentals of the industry, in enhancing facility operations, in diversifying contractual techniques, and in developing industry positions to be taken in international agencies. As a member of the IOPC Fund since June 2007, the GIIGNL prepared this LNG overview in order to offer a better understanding to state delegations about this specific product and its market and to contribute to the debate on the implementation of the HNS Convention. the first chapter constitutes an introduction to the LNG Industry: presentation of an LNG Chain, overview of the global LNG trade and its growth rate, type of contracts, LNG tankers and technical transportation constraints, liquefaction and re-gasification plants around the world. The second chapter focuses on some singularities of the LNG industry that differentiate LNG from other Hazardous and Noxious Substances: LNG, a clean and unique product and activity, high standards and firm regulations concerning security and maritime safety, high level of investment required for an LNG chain, DES and FOB, the fundamental Incoterms of LNG sales and purchase. The third chapter presents the HNS Convention as potentially applicable to the LNG market: a two tier compensation regime - a new perspective for the LNG industry, a potential impact on LNG sales and purchase agreements, the importance of global HNS ratification within LNG

  14. Periodic solutions of singular second order differential equations : upper and lower functions

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Torres, P.J.; Zamora, M.

    2011-01-01

    Roč. 74, č. 18 (2011), s. 7078-7093 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order differential equation * singularity at the phase variable * Rayleigh-Plesset equation Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11005049

  15. The Cucker-Smale Equation: Singular Communication Weight, Measure-Valued Solutions and Weak-Atomic Uniqueness

    Science.gov (United States)

    Mucha, Piotr B.; Peszek, Jan

    2018-01-01

    The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency, e.g. to aggregate, flock or disperse. This paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space {C_{weak}(0,∞M)}. The solution is defined as a mean-field limit of the empirical distributions of particles, the dynamics of which is governed by the Cucker-Smale particle system. The studied communication weight is {ψ(s)=|s|^{-α}} with {α \\in (0,1/2)}. This range of singularity admits the sticking of characteristics/trajectories. The second result concerns the weak-atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form {m_i δ_{x_i} ⊗ δ_{v_i}}, preserves its atomic structure. Hence these coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.

  16. Soliton solutions of the resonant nonlinear Schrödinger's equation in optical fibers with time-dependent coefficients by simplest equation approach

    Science.gov (United States)

    Eslami, M.; Mirzazadeh, M.; Biswas, Anjan

    2013-11-01

    In this paper, the resonant nonlinear Schrödinger's equation is studied with four forms of nonlinearity. This equation is also considered with time-dependent coefficients. The simplest equation method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.

  17. KP solitons, total positivity, and cluster algebras

    Science.gov (United States)

    Kodama, Yuji; Williams, Lauren K.

    2011-01-01

    Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539–541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solutions that one obtains in this way come from points of the totally nonnegative part of the Grassmannian. In this paper we explain how the theory of total positivity and cluster algebras provides a framework for understanding these soliton solutions to the KP equation. We then use this framework to give an explicit construction of certain soliton contour graphs and solve the inverse problem for soliton solutions coming from the totally positive part of the Grassmannian. PMID:21562211

  18. The approximate solution of singular integro-differential equations systems on smooth contours in spaces Lp

    OpenAIRE

    Iu. Caraus

    1997-01-01

    This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE) in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a s...

  19. Singular Perturbation Based Solution to Optimal Microalgal Growth Problem and Its Infinite Time Horizon Analysis

    Czech Academy of Sciences Publication Activity Database

    Čelikovský, Sergej; Papáček, Štěpán; Cervantes-Herrera, A.; Ruiz-León, J.

    2010-01-01

    Roč. 55, č. 3 (2010), s. 767-772 ISSN 0018-9286 R&D Projects: GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z50200510 Keywords : Photosynthetic factory (PSF) * singular perturbation * optimal control Subject RIV: BC - Control Systems Theory Impact factor: 1.950, year: 2010 http://library.utia.cas.cz/separaty/2010/TR/celikovsky-0342103.pdf

  20. Spacetime Singularity Resolution by M-Theory Fivebranes: Calibrated Geometry, Anti-de Sitter Solutions and Special Holonomy Metrics

    Science.gov (United States)

    Conamhna, Oisín A. P. Mac

    2008-12-01

    The supergravity description of various configurations of supersymmetric M-fivebranes wrapped on calibrated cycles of special holonomy manifolds is studied. The description is provided by solutions of eleven-dimensional supergravity which interpolate smoothly between a special holonomy manifold and an event horizon with Anti-de Sitter geometry. For known examples of Anti-de Sitter solutions, the associated special holonomy metric is derived. One explicit Anti-de Sitter solution of M-theory is so treated for fivebranes wrapping each of the following cycles: Kähler cycles in Calabi-Yau two, three- and four-folds; special lagrangian cycles in three- and four-folds; associative three- and co-associative four-cycles in G 2 manifolds; complex lagrangian four-cycles in Sp(2) manifolds; and Cayley four-cycles in Spin(7) manifolds. In each case, the associated special holonomy metric is singular, and is a hyperbolic analogue of a known metric. The analogous known metrics are respectively: Eguchi-Hanson, the resolved conifold and the four-fold resolved conifold; the deformed conifold, and the Stenzel four-fold metric; the Bryant-Salamon-Gibbons-Page-Pope G 2 metrics on an {mathbb{R}^4} bundle over S 3, and an {mathbb{R}^3} bundle over S 4 or {mathbb{CP}^2} ; the Calabi hyper-Kähler metric on {T^*mathbb{CP}^2} ; and the Bryant-Salamon-Gibbons-Page-Pope Spin(7) metric on an {mathbb{R}^4} bundle over S 4. By the AdS/CFT correspondence, a conformal field theory is associated to each of the new singular special holonomy metrics, and defines the quantum gravitational physics of the resolution of their singularities.

  1. Ring vortex solitons in nonlocal nonlinear media

    DEFF Research Database (Denmark)

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

    2005-01-01

    We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... 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....

  2. Time-space noncommutative Abelian solitons

    International Nuclear Information System (INIS)

    Chu, C.-S.; Lechtenfeld, Olaf

    2005-01-01

    We demonstrate the construction of solitons for a time-space Moyal-deformed integrable U(n) sigma model (the Ward model) in 2+1 dimensions. These solitons cannot travel parallel to the noncommutative spatial direction. For the U(1) case, the rank-one single-soliton configuration is constructed explicitly and is singular in the commutative limit. The projection to 1+1 dimensions transforms it to a noncommutative instanton-like configuration. The latter is governed by a new integrable equation, which describes a Moyal-deformed sigma model with a particular Euclidean metric and a magnetic field

  3. Hairy AdS solitons

    Energy Technology Data Exchange (ETDEWEB)

    Anabalón, Andrés, E-mail: andres.anabalon@uai.cl [Departamento de Ciencias, Facultad de Artes Liberales and Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Astefanesei, Dumitru, E-mail: dumitru.astefanesei@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Choque, David, E-mail: brst1010123@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso (Chile)

    2016-11-10

    We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.

  4. 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.

  5. Soliton-like solutions of a generalized variable-coefficient higher order nonlinear Schroedinger equation from inhomogeneous optical fibers with symbolic computation

    International Nuclear Information System (INIS)

    Li Juan; Zhang Haiqiang; Xu Tao; Zhang, Ya-Xing; Tian Bo

    2007-01-01

    For the long-distance communication and manufacturing problems in optical fibers, the propagation of subpicosecond or femtosecond optical pulses can be governed by the variable-coefficient nonlinear Schroedinger equation with higher order effects, such as the third-order dispersion, self-steepening and self-frequency shift. In this paper, we firstly determine the general conditions for this equation to be integrable by employing the Painleve analysis. Based on the obtained 3 x 3 Lax pair, we construct the Darboux transformation for such a model under the corresponding constraints, and then derive the nth-iterated potential transformation formula by the iterative process of Darboux transformation. Through the one- and two-soliton-like solutions, we graphically discuss the features of femtosecond solitons in inhomogeneous optical fibers

  6. Homotopy and solitons. 1

    International Nuclear Information System (INIS)

    Boya, L.J.; Carinena, J.F.; Mateos, J.

    1978-01-01

    Starting from classical field theory with a Lagrangian, solitons are identified with solutions of the field equations which satisfy peculiar boundary conditions. The symmetry group which causes the degenerate vacuum is taken generally internal, that is, not operating in space-time. Gauge symmetry plays a dominant role. A precise definition of solitons is given and it is shown how to study some continuous mappings of the ''distant'' parts of space on the set of degenerate vacua. A marvellous instrument, the exact homotopy sequence, is applied to calculate homotopy groups of some higher-dimensional manifolds

  7. Soliton trains in motion

    International Nuclear Information System (INIS)

    Hause, A.; Mitschke, F.

    2010-01-01

    Two solitons in an optical fiber can form pairs in which the double-humped shape is maintained even when the pair is shifted in frequency by the Raman effect. We show here analytically that this is possible even when the two solitons have unequal power. We discuss the forces that cause relative motion of the two solitons, and determine a condition for balance, i.e., for a pair to maintain their separation while the phase keeps evolving. At a specific parameter point we find a solution in which even the phase profile of the pulse pair is maintained. We then discuss that this special point exists also for multipeak structures, or soliton trains. These trains can move as an entity due to Raman shifting. The results are tested by numerical simulation. A comparison to literature reveals that both the rotating phase pair and the constant phase soliton pair apparently have been seen before by others in numerical simulations. Our treatment provides the general framework.

  8. New analytical solution for solving steady-state heat conduction problems with singularities

    Directory of Open Access Journals (Sweden)

    Laraqi Najib

    2013-01-01

    Full Text Available A problem of steady-state heat conduction which presents singularities is solved in this paper by using the conformal mapping method. The principle of this method is based on the Schwarz-Christoffel transformation. The considered problem is a semi-infinite medium with two different isothermal surfaces separated by an adiabatic annular disc. We show that the thermal resistance can be determined without solving the governing equations. We determine a simple and exact expression that provides the thermal resistance as a function of the ratio of annular disc radii.

  9. Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

    Directory of Open Access Journals (Sweden)

    George N. Galanis

    2005-10-01

    Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0solutions of the above boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

  10. Soliton solutions of the generalized sinh-Gordon equation by the ...

    Indian Academy of Sciences (India)

    substituting αm,...,v and the general solutions of eq. (8) into (7) we have more travelling wave solutions of the nonlinear evolution eq. (1). 3. Application to the generalized sinh-Gordon equation. First, consider the following transformation: ξ = λ(x + ct), η = λ (x + a ct) , a = c2,. (9) where λ, c are two parameters to be determined.

  11. Exact bright and dark spatial soliton solutions in saturable nonlinear media

    International Nuclear Information System (INIS)

    Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

    2009-01-01

    We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

  12. Soliton-soliton effective interaction

    International Nuclear Information System (INIS)

    Maki, J.N.

    1986-01-01

    A scheme of semi-phenomenological quantization is proposed for the collision process of two equal size envelopes-solitons provided by nonlinear Schroedinger equation. The time advance due to two envelopes-solitons collision was determined. Considering the solitons as puntual particles and using the description of classical mechanics, the effective envelope soliton-envelope soliton attractive potential, denominated modified Poschl-Teller potential. The obtainment of this potential was possible using the information in from of system memory, done by an analytical expression of time delay. Such system was quantized using this effective potential in Schroeding equation. The S col matrix of two punctual bodies was determined, and it is shown that, in the limit of 1 2 2 /mN 4 it reproduces the exact S 2N matrix obtained from soliton packet wich incurs on another soliton packet. Every ones have the same mass, interacts by contact force between two bodies. These packets have only one bound state, i e, do not have excited states. It was verified that, using the S col matrix, the binding energy of ground state of the system can be obtained, which is coincident with 2N particles in the 1/N approximation. In this scheme infinite spurious bound states are found (M.C.K.) [pt

  13. Nontopological solitons

    International Nuclear Information System (INIS)

    Friedberg, R.

    1977-01-01

    It is pointed out that the study of solitons offers a new departure for the problem of handling bound states in relativistic quantum field theory which has hampered development of a simple conventional model of hadrons. The principle is illustrated by the case of a quantum mechanical particle moving in two dimensions under the centrally symmetric and quasi-harmonic potential. Restriction is made to nontopological solitons. These ideas are applied to a model of hadrons. 10 references

  14. Inelastic Vector Soliton Collisions: A Lattice-Based Quantum Representation

    National Research Council Canada - National Science Library

    Vahala, George; Vahala, Linda; Yepez, Jeffrey

    2004-01-01

    .... Under appropriate conditions the exact 2-soliton vector solutions yield in elastic soliton collisions, in agreement with the theoretical predictions of Radhakrishnan et al. (1997 Phys. Rev. E56, 2213...

  15. Abelian solutions of the soliton equations and Riemann-Schottky problems

    Science.gov (United States)

    Krichever, Igor M.

    2008-12-01

    The present article is an exposition of the author's talk at the conference dedicated to the 70th birthday of S.P. Novikov. The talk contained the proof of Welters' conjecture which proposes a solution of the classical Riemann-Schottky problem of characterizing the Jacobians of smooth algebraic curves in terms of the existence of a trisecant of the associated Kummer variety, and a solution of another classical problem of algebraic geometry, that of characterizing the Prym varieties of unramified covers.

  16. The approximate solution of singular integro-differential equations systems on smooth contours in spaces Lp

    Directory of Open Access Journals (Sweden)

    Iu. Caraus

    1997-08-01

    Full Text Available This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a smooth Jordan border limiting the one-spanned area $F^{+}$, containing a point $ t=0$, $ F^{-}= C \\setminus \\{ F^{+}\\cup \\Gamma \\}$, $C $ is a full complex plane. Let $z= \\psi (w-$ be a function, mapping comformally and single-valuedly the surface $\\Gamma_{0}=\\{|w| >1 \\} $ on $F^{-} $ so that $ \\psi (\\infty = \\infty ,\\psi^{ (\\prime }(\\infty >0$. We shall assume that the function $ z= \\psi (w$ has its second derivative, satisfying on $\\Gamma_{0} $ the H\\"older condition with some parameter $ \

  17. Soliton equations and pseudospherical surfaces

    International Nuclear Information System (INIS)

    Sasaki, R.

    1979-03-01

    All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)

  18. Soliton turbulence in shallow water ocean surface waves.

    Science.gov (United States)

    Costa, Andrea; Osborne, Alfred R; Resio, Donald T; Alessio, Silvia; Chrivì, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E

    2014-09-05

    We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ∼ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ∼ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.

  19. Enhancement accuracy of approximated solutions of the nonlinear singular integral equations of Chew-Low type

    International Nuclear Information System (INIS)

    Zhidkov, E.P.; Nguen Mong; Khoromskij, B.N.

    1979-01-01

    The ways of enhancement of the accuracy of approximate solutions of the Chew-Low type equation are considered. Difference schemes are proposed which allow one to obtain solution expansion in degrees of lattice step. On the basis of the expansion by the Richardson method the refinement of approximated solutions is made. Besides, the iteration process is constructed which reduces immediately to the solution of enhanced accuracy. The efficiency of the methods proposed is illustrated by numerical examples

  20. Canard solution and its asymptotic approximation in a second-order nonlinear singularly perturbed boundary value problem with a turning point

    Science.gov (United States)

    Shen, Jianhe; Han, Maoan

    2014-08-01

    This paper considers the existence and uniformly valid asymptotic approximation of canard solutions in a second-order nonlinear singularly perturbed boundary value problem with a turning point. We get the main results by constructing the asymptotic solution first and then defining a couple of upper and lower solutions suitably on the basis of the asymptotic solution. Two examples are carried out to illustrate and verify the theoretical results.

  1. Gravitational generation of mass in soliton theory

    International Nuclear Information System (INIS)

    Kozhevnikov, I.R.; Rybakov, Yu.P.

    1985-01-01

    It is shown that in the framework of a simple scalar field model, that admits soliton solutions, with gravitational field interactions being specially included, one succeeds in ensuring for a scalar field a correct spacial asymptotics that depends on the system mass. Theory, the quantum relation of a corpuscular-wave dualism is fulfilled for soliton solutions in such a model

  2. Soliton solutions of coupled systems by improved (G'/G)-expansion method

    Science.gov (United States)

    Mohyud-Din, Syed Tauseef; Shakeel, Muhammad

    2013-10-01

    The paper witnesses the extension of improved (G'/G)-expansion method to generate traveling wave solutions of coupled systems. The proposed algorithm is extremely effective and is tested on two very important systems (namely coupled Higgs and Maccari equations) in mathematical physics. Numerical results reflect complete compatibility of suggested scheme.

  3. Lie symmetry analysis and soliton solutions of time-fractional K (m, n ...

    Indian Academy of Sciences (India)

    In this note, method of Lie symmetries is applied to investigate symmetry properties of timefractional K ( m , n ) equation with the Riemann–Liouville derivatives. Reduction of time-fractional K ( m , n ) equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α. Thensoliton solutions ...

  4. Nodal soliton solutions for quasilinear Schrödinger equations with critical exponent

    Science.gov (United States)

    Deng, Yinbin; Peng, Shuangjie; Wang, Jixiu

    2013-01-01

    This paper is concerned with constructing nodal radial solutions for quasilinear Schrödinger equations in {R}^N with critical growth which have appeared as several models in mathematical physics. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem. Since the critical exponent appears and the lower order term may change sign, we should use more delicate arguments.

  5. Nodal soliton solutions for generalized quasilinear Schrödinger equations

    Energy Technology Data Exchange (ETDEWEB)

    Deng, Yinbin, E-mail: ybdeng@mail.ccnu.edu.cn; Peng, Shuangjie, E-mail: sjpeng@mail.ccnu.edu.cn [School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079 (China); Wang, Jixiu, E-mail: wangjixiu127@aliyun.com [School of Mathematics and Computer Science, Hubei University of Arts and Science, Xiangyang 441053 (China)

    2014-05-15

    This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in R{sup N} which arise from plasma physics, fluid mechanics, as well as high-power ultashort laser in matter. For any given integer k ⩾ 0, by using a change of variables and minimization argument, we obtain a sign-changing minimizer with k nodes of a minimization problem.

  6. 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...... mechanically without approximations, and their numerical solutions at different temperatures are presented. Our conclusion is that the Davydov soliton is stable at 310 K....

  7. FN approximation of the solution to a singular integral equation of classical reactor physics

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2004-01-01

    The iterated FN method is applied to a singular integral equation arising from a classical problem of reactor physics to determine the distribution of fissile material giving a spatially uniform flux. The FN iterations are accelerated toward convergence through the Wynn-algorithm - but first - Happy Birthday 'Fast Eddie' Larsen Why do I refer to the well known, most proper and exquisitely accomplished Edward W. Larsen as 'Fast Eddie'. Well our story begins in a small back bar room in the lobby of one of Los Alamos' finest and most luxurious hotels. Two young men were having a transport theoretic discussion while they were engaged in a serious game of pool with monetary benefits going to the winner. In addition, the two were sipping their most favorite lavation in rather large quantities - one, a short stocky man with thinning hair, was sipping to forget the cost of his recent divorce, and the other, a shorter stockier man also with thinning hair, was drinking, well because he liked to drink and it just made him silly. As they continued their transport discussion, one stocky man turned to the other and said, 'I wonder what 'Fast Eddie' Larsen would say to our transport question'. The other stocky man immediately thought the 'Fast Eddie' reference was to Paul Newman who played 'Fast Eddie', an expert at applied particle transport theory (a pool player) in the movie the Hustler and asked if indeed this was the case. The first stocky man said 'No. I call everyone with the name Ed 'Fast Eddie' ' - and that's the story of how 'Fast Eddie' Larsen got his name. Happy 60th Ed and thanks for all the great transport theory - from one of your biggest fans

  8. FN approximation of the solution to a singular integral equation of classical reactor physics

    Energy Technology Data Exchange (ETDEWEB)

    Ganapol, B.D. [Department of Aerospace and Mechanical Engineering, University of Arizona, AME Building, Tucson, AZ 85721 (United States)]. E-mail: ganapol@ame.arizona.edu

    2004-11-01

    The iterated FN method is applied to a singular integral equation arising from a classical problem of reactor physics to determine the distribution of fissile material giving a spatially uniform flux. The FN iterations are accelerated toward convergence through the Wynn-algorithm - but first - Happy Birthday 'Fast Eddie' Larsen Why do I refer to the well known, most proper and exquisitely accomplished Edward W. Larsen as 'Fast Eddie'. Well our story begins in a small back bar room in the lobby of one of Los Alamos' finest and most luxurious hotels. Two young men were having a transport theoretic discussion while they were engaged in a serious game of pool with monetary benefits going to the winner. In addition, the two were sipping their most favorite lavation in rather large quantities - one, a short stocky man with thinning hair, was sipping to forget the cost of his recent divorce, and the other, a shorter stockier man also with thinning hair, was drinking, well because he liked to drink and it just made him silly. As they continued their transport discussion, one stocky man turned to the other and said, 'I wonder what 'Fast Eddie' Larsen would say to our transport question'. The other stocky man immediately thought the 'Fast Eddie' reference was to Paul Newman who played 'Fast Eddie', an expert at applied particle transport theory (a pool player) in the movie the Hustler and asked if indeed this was the case. The first stocky man said 'No. I call everyone with the name Ed 'Fast Eddie' ' - and that's the story of how 'Fast Eddie' Larsen got his name. Happy 60th Ed and thanks for all the great transport theory - from one of your biggest fans.

  9. Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons piloted (controlled) by corresponding solutions of associated linear Klein-Gordon and Schroedinger equations

    International Nuclear Information System (INIS)

    Vigier, J.P.

    1991-01-01

    Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, Nelson, de Broglie, Guerra et al.), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm real trajectories associated with linear solutions of the usual Schroedinger and Klein-Gordon equations

  10. Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

    International Nuclear Information System (INIS)

    Liu Wenjun; Tian Bo; Xu Tao; Sun Kun; Jiang Yan

    2010-01-01

    Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.

  11. An(1) Toda solitons and the dressing symmetry

    International Nuclear Information System (INIS)

    Belich, H.; Paunov, R.

    1996-12-01

    We present an elementary derivation of the soliton-like solutions in the A n (1) Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which by dressing group action, produces a generic soliton solution. In the particular example of mono solitons we suggest a relation to vertex operator formalism, previously used by olive, Turok and Underwood. Our results can also be considered as generalization of the approach to the sine-Gordon solitons, proposed by Babelon and Bernard. (author)

  12. Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations

    International Nuclear Information System (INIS)

    Fiedler, B.; Schimming, R.

    1983-01-01

    The fourth order field equations proposed by TREDER with a linear combination of BACH's tensor and EINSTEIN's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry. (author)

  13. Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations

    Energy Technology Data Exchange (ETDEWEB)

    Fiedler, B.; Schimming, R.

    1983-01-01

    The fourth order field equations proposed by TREDER with a linear combination of BACH's tensor and EINSTEIN's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry.

  14. Supergravity solitons

    International Nuclear Information System (INIS)

    Aichelburg, P.C.; Embacher, F.

    1987-01-01

    The Langrangian for a single free soliton in N = 2 supergravity as proposed in an earlier paper, is studied. We analyze the algebra of constraints and discuss the local gauge symmetry due to the existence of first class constraints. The classical motion as well as a Gupta-Bleuler type quantization are given. (Author)

  15. Soliton turbulence

    Science.gov (United States)

    Tchen, C. M.

    1986-01-01

    Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.

  16. Performance Prediction Network for Serial Manipulators Inverse Kinematics solution Passing Through Singular Configurations

    Directory of Open Access Journals (Sweden)

    Ali T. Hasan

    2011-01-01

    Full Text Available This paper is devoted to the application of Artificial Neural Networks (ANN to the solution of the Inverse Kinematics (IK problem for serial robot manipulators, in this study two networks were trained and compared to examine the effect of considering the Jacobian Matrix to the efficiency of the IK solution. Given the desired trajectory of the end effector of the manipulator in a free-of-obstacles workspace, Offline smooth geometric paths in the joint space of the manipulator are obtained. Even though it is very difficult in practice, data used in this study were recorded experimentally from sensors fixed on robot's joints to overcome the effect of kinematics uncertainties presence in the real world such as ill-defined linkage parameters, links flexibility and backlashes in gear train The generality and efficiency of the proposed algorithm are demonstrated through simulations of a general six DOF serial robot manipulator, finally the obtained results have been verified experimentally.

  17. Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations

    Science.gov (United States)

    Fiedler, B.; Schimming, R.

    A formal power series ansatz is used to obtain a convergence proof that the fourth-order gravitational field equations proposed by Treder (1977) with a linear combination of Bach's (1921) tensor and Einstein's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and nonflat in some neighborhood of the center of symmetry. Conformal invariance is attained by means of a scalar gauge field.

  18. 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...... 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....

  19. Black holes, dark wormholes, and solitons in f (T ) gravities

    Science.gov (United States)

    Mai, Zhan-Feng; Lü, H.

    2017-06-01

    By choosing an appropriate vielbein basis, we obtain a class of spherically-symmetric solutions in f (T ) gravities. The solutions are asymptotic to Minkowski spacetimes with leading falloffs the same as those of the Schwarzschild black hole. In general, these solutions have branch-cut singularities in the middle. For appropriately chosen f (T ) functions, extremal black holes can also emerge. Furthermore, we obtain wormhole configurations whose spatial section is analogous to an Ellis wormhole, but -gt t runs from 0 to 1 as the proper radial coordinate runs from -∞ to +∞ . Thus a signal sent from -∞ to +∞ through the wormhole will be infinitely red-shifted. We call such a spacetime configuration a dark wormhole. By introducing a bare cosmological constant Λ0, we construct smooth solitons that are asymptotic to local AdS with an effective Λeff. In the middle of bulk, the soliton metric behaves like the AdS of bare Λ0 in global coordinates. We also embed AdS planar and Lifshitz black holes in f (T ) gravities. Finally we couple the Maxwell field to the f (T ) theories and construct electrically-charged solutions.

  20. Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

    Science.gov (United States)

    Le Coz, Stefan; Tsai, Tai-Peng

    2014-11-01

    We look for solutions to general nonlinear Schrödinger equations built upon solitons and kinks. Solitons are localized solitary waves, and kinks are their non-localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of Lp - Lp‧ dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.

  1. Limit Properties of Solutions of Singular Second-Order Differential Equations

    Directory of Open Access Journals (Sweden)

    Weinmüller Ewa

    2009-01-01

    Full Text Available We discuss the properties of the differential equation , a.e. on , where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is given. We also describe the structure of boundary conditions which are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.

  2. Multiple positive solutions to third-order three-point singular ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    and (H1), one can conclude that A j λ is continuous and compact from Q to Q. 2. Therefore, x ∈ Q is a solution of (2) if x is a fixed point of A j λ on Q. Then we next consider the existence of fixed point of A j λ on Q. Lemma 2.3. For each r > 0, there exists λ(r) > 0 such that i(A j λ. ,Qr, Q) = 1,. ∀λ ∈ (0, λ(r )), j ∈ N, where Qr = {x ...

  3. Existence of solutions to nonlocal and singular elliptic problems via Galerkin method

    Directory of Open Access Journals (Sweden)

    Francisco Julio S. A. Correa

    2004-02-01

    Full Text Available We study the existence of solutions to the nonlocal elliptic equation $$ -M(|u|^2Delta u = f(x,u $$ with zero Dirichlet boundary conditions on a bounded and smooth domain of $mathbb{R}^n$. We consider the $M$-linear case with $fin H^{-1}(Omega $, and the sub-linear case $f(u=u^{alpha}$, $0

  4. Solitons in relativistic cosmologies

    International Nuclear Information System (INIS)

    Pullin, J.

    1988-08-01

    The application to the construction of solitonic cosmologies in General Relativity of the Inverse Scattering Technique of Belinskii an Zakharov is analyzed. Three improvements to the mentioned technique are proposed: the inclusion of higher order poles in the scattering matrix, a new renormalization technique for diagonal metrics and the extension of the technique to include backgrounds with material content by means of a Kaluza-Klein formalism. As a consequence of these improvements, three new aspects can be analyzed: a) The construction of anisotropic and inhomogeneous cosmological models which can mimic the formation of halos and voids, due to the presence of a material content. The new renormalization technique allows to construct an exact perturbation theory. b) The analysis of the dynamics of models with cosmological constant (inflationary models) and their perturbations. c) The study of interaction of gravitational solitonic waves on material backgrounds. Moreover, some additional works, connected with the existance of 'Crack of doom' type singularities in Kaluza-Klein cosmologies, stochastic perturbations in inflationary universes and inflationary phase transitions in rotating universes are described. (Author) [es

  5. Vector pulsing soliton of self-induced transparency in waveguide

    International Nuclear Information System (INIS)

    Adamashvili, G.T.

    2015-01-01

    A theory of an optical resonance vector pulsing soliton in waveguide is developed. A thin transition layer containing semiconductor quantum dots forms the boundary between the waveguide and one of the connected media. Analytical and numerical solutions for the optical vector pulsing soliton in waveguide are obtained. The vector pulsing soliton in the presence of excitonic and bi-excitonic excitations is compared with the soliton for waveguide TM-modes with parameters that can be used in modern optical experiments. It is shown that these nonlinear waves have significantly different parameters and shapes. - Highlights: • An optical vector pulsing soliton in a planar waveguide is presented. • Explicit form of the optical vector pulsing soliton are obtained. • The vector pulsing soliton and the soliton have different parameters and profiles

  6. High precision series solutions of differential equations: Ordinary and regular singular points of second order ODEs

    Science.gov (United States)

    Noreen, Amna; Olaussen, Kåre

    2012-10-01

    A subroutine for a very-high-precision numerical solution of a class of ordinary differential equations is provided. For a given evaluation point and equation parameters the memory requirement scales linearly with precision P, and the number of algebraic operations scales roughly linearly with P when P becomes sufficiently large. We discuss results from extensive tests of the code, and how one, for a given evaluation point and equation parameters, may estimate precision loss and computing time in advance. Program summary Program title: seriesSolveOde1 Catalogue identifier: AEMW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 991 No. of bytes in distributed program, including test data, etc.: 488116 Distribution format: tar.gz Programming language: C++ Computer: PC's or higher performance computers. Operating system: Linux and MacOS RAM: Few to many megabytes (problem dependent). Classification: 2.7, 4.3 External routines: CLN — Class Library for Numbers [1] built with the GNU MP library [2], and GSL — GNU Scientific Library [3] (only for time measurements). Nature of problem: The differential equation -s2({d2}/{dz2}+{1-ν+-ν-}/{z}{d}/{dz}+{ν+ν-}/{z2})ψ(z)+{1}/{z} ∑n=0N vnznψ(z)=0, is solved numerically to very high precision. The evaluation point z and some or all of the equation parameters may be complex numbers; some or all of them may be represented exactly in terms of rational numbers. Solution method: The solution ψ(z), and optionally ψ'(z), is evaluated at the point z by executing the recursion A(z)={s-2}/{(m+1+ν-ν+)(m+1+ν-ν-)} ∑n=0N Vn(z)A(z), ψ(z)=ψ(z)+A(z), to sufficiently large m. Here ν is either ν+ or ν-, and Vn(z)=vnz. The recursion is initialized by A(z)=δzν,for n

  7. Solitons in an isolated helix chain

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Zolotaryuk, Alexander; Savin, A.V.

    1997-01-01

    -, and third-nearest neighbors. The set of nonlinear field equations with respect to the longitudinal and transverse (torsional and radial) displacements of the chain molecules has been derived and treated. Stable nontopological soliton solutions which describe supersonic pulses of longitudinal compression...... propagating together with localized transverse thickening (bulge) and torsional stretching (untwisting) have been found. The stability properties of these (three-component) soliton solutions have been studied by using numerical techniques developed for seeking solitary-wave solutions in complex molecular...

  8. An improved solution of local window parameters setting for local singularity analysis based on Excel VBA batch processing technology

    Science.gov (United States)

    Zhang, Daojun; Cheng, Qiuming; Agterberg, Frits; Chen, Zhijun

    2016-03-01

    In this paper Excel VBA is used for batch calculation in Local Singularity Analysis (LSA), which is for the information extracting from different kinds of geoscience data. Capabilities and advantages of a new module called Batch Tool for Local Singularity Index Mapping (BTLSIM) are: (1) batch production of series of local singularity maps with different settings of local window size, shape and orientation parameters; (2) local parameter optimization based on statistical tests; and (3) provision of extra output layers describing how spatial changes induced by parameter optimization are related to spatial structure of the original input layers.

  9. The wrinkle-like N-solitons for the thermophoretic motion equation through graphene sheets

    Science.gov (United States)

    Ma, Yu-Lan; Li, Bang-Qing

    2018-03-01

    The main work is focused on the thermophoretic motion equation, which was derived from wrinkle wave motions in substrate-supported graphene sheets. Via the bilinear method, a class of wrinkle-like N-soliton solutions is constructed. The one-soliton, two-soliton and three-soliton are observed graphically. The shape, amplitude, open direction and width of the N-solitons are controllable through certain parameters.

  10. Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point

    Energy Technology Data Exchange (ETDEWEB)

    Shu, Fu-Wen [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University,Nanchang 330031 (China); Lin, Kai [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); Instituto de Física, Universidade de São Paulo,CP 66318, 05315-970, São Paulo (Brazil); Wang, Anzhong [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China); GCAP-CASPER, Physics Department, Baylor University,Waco, TX 76798-7316 (United States); Wu, Qiang [Institute for Advanced Physics Mathematics, Zhejiang University of Technology,Hangzhou 310032 (China)

    2014-04-08

    In this paper, we study static vacuum solutions of quantum gravity at a fixed Lifshitz point in (2+1) dimensions, and present all the diagonal solutions in closed forms in the infrared limit. The exact solutions represent spacetimes with very rich structures: they can represent generalized BTZ black holes, Lifshitz space-times or Lifshitz solitons, in which the spacetimes are free of any kind of space-time singularities, depending on the choices of the free parameters of the solutions. We also find several classes of exact static non-diagonal solutions, which represent similar space-time structures as those given in the diagonal case. The relevance of these solutions to the non-relativistic Lifshitz-type gauge/gravity duality is discussed.

  11. Optical spatial solitons: historical overview and recent advances

    Science.gov (United States)

    Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N.

    2012-08-01

    Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a

  12. Topological solitons in DNA with modified potential

    Directory of Open Access Journals (Sweden)

    E Behjat

    2010-06-01

    Full Text Available DNA is not only an essential research subject for biologists, but also it raises very interesting questions for physicists.The open states in DNA double helix can lead to topological solitons. Since DNA is a very long molecule of order a meter or so long and nano-scale width, solitons can propagate along the molecule. In this paper, considering a correction term in the interaction potential between two chains, we study the dispersion relation analytically, and obtain the soliton solutions using a new relaxation method. Then we compare our solutions and its energy with those obtained by others without the proposed correction term.

  13. Nonlinear Dynamics: Maps, Integrators and Solitons

    Energy Technology Data Exchange (ETDEWEB)

    Parsa, Z.

    1998-10-01

    For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.

  14. Vacuum-induced jitter in spatial solitons.

    Science.gov (United States)

    Nagasako, E; Boyd, R; Agarwal, G S

    1998-08-31

    We perform a calculation to determine how quantum mechanical fluctuations influence the propagation of a spatial soliton through a nonlinear material. To do so, we derive equations of motion for the linearized operators describing the deviation of the soliton position and transverse momentum from those of a corresponding classical solution to the nonlinear wave equation, and from these equations we determine the quantum uncertainty in the soliton position and transverse momentum. We find that under realistic laboratory conditions the quantum uncertainty in position is several orders of magnitude smaller the classical width of the soliton. This result suggests that the reliability of photonic devices based on spatial solitons is not compromised by quantum fluctuations.

  15. Quantum deflation of classical solitons

    International Nuclear Information System (INIS)

    Sveshnikov, K.; Silaev, P.

    1996-01-01

    It is shown, that due to nonperturbative effects, in the relativistic QFT the extended particle-like solutions should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytical and numerical results for the dynamics of such a process are given for 1 + 1 dimensional soliton models

  16. Soliton concepts and protein structure

    Science.gov (United States)

    Krokhotin, Andrei; Niemi, Antti J.; Peng, Xubiao

    2012-03-01

    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 that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find 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 compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

  17. Soliton interactions and complexes for coupled nonlinear Schrödinger equations.

    Science.gov (United States)

    Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan

    2012-03-01

    Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.

  18. Dynamical behaviours and exact travelling wave solutions of ...

    Indian Academy of Sciences (India)

    Modified generalized Vakhnenko equation; cusped solitons; loop solitons; periodic cusp wave solutions; smooth periodic wave solutions; pseudopeakon solitons; ... Guangxi 541004, People's Republic of China; School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, ...

  19. Rational solitons in the parity-time-symmetric nonlocal nonlinear Schrödinger model

    International Nuclear Information System (INIS)

    Li Min; Xu Tao; Meng Dexin

    2016-01-01

    In this paper, via the generalized Darboux transformation, rational soliton solutions are derived for the parity-time-symmetric nonlocal nonlinear Schrödinger (NLS) model with the defocusing-type nonlinearity. We find that the first-order solution can exhibit the elastic interactions of rational antidark-antidark, dark-antidark, and antidark-dark soliton pairs on a continuous wave background, but there is no phase shift for the interacting solitons. Also, we discuss the degenerate case in which only one rational dark or antidark soliton survives. Moreover, we reveal that the second-order rational solution displays the interactions between two solitons with combined-peak-valley structures in the near-field regions, but each interacting soliton vanishes or evolves into a rational dark or antidark soliton as |z| → ∞. In addition, we numerically examine the stability of the first- and second-order rational soliton solutions. (author)

  20. Solitons in Gross-Pitaevskii equation

    International Nuclear Information System (INIS)

    Lopes, E.

    1985-01-01

    It is observed that, when the potential is integrable and repulsive, the Gross-Pitaevskii Equation, with non-vanishing boundary conditions, describes a family of planar solitons. A method is presented which provides an exact soliton field to the Dirac Delta potential and an approximation solution to any other kind of potential. As an example the method is then applied to the case of a repulsive Yukawa potential. A brief discuss the relation between these solitons and Anderson's superfluidity mechanism, is also presented. (author) [pt

  1. Topological Solitons in Physics.

    Science.gov (United States)

    Parsa, Zohreh

    1979-01-01

    A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)

  2. Helmholtz solitons in power-law optical materials

    International Nuclear Information System (INIS)

    Christian, J. M.; McDonald, G. S.; Potton, R. J.; Chamorro-Posada, P.

    2007-01-01

    A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures the evolution of broad beams at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses, and liquid crystals. Exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three general conservation laws are also reported. Analysis and numerical simulations examine the stability of the Helmholtz power-law solitons. A propagation feature, associated with spatial solitons in power-law media, constituting a class of oscillatory solution, is identified

  3. Soliton-based ultra-high speed optical communications

    Indian Academy of Sciences (India)

    evolution of information and introduction of optical soliton solution as the stable nonlinear solution. The paper ... aged solitons will be presented to demonstrate the effectiveness of dispersion management techniques both .... Most high speed transmission systems at present use an all optical scheme with loss compensated ...

  4. Solitons and instantons

    International Nuclear Information System (INIS)

    Rajaraman, R.

    1982-01-01

    In recent years, a host of new non-perturbative results in relativistic quantum field theory have been obtained, based on classical soliton and instanton solutions. This book offers an elementary and unified introduction to these developments. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunnelling, theta-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective coordinates etc. are developed from the very outset. The presentation of this work is kept at a fairly simple level, and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. The book is mainly addressed to particle physicists and quantum field theorists. (Auth.)

  5. Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

    Science.gov (United States)

    Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

    2018-04-01

    The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

  6. Plane waves with weak singularities

    International Nuclear Information System (INIS)

    David, Justin R.

    2003-03-01

    We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)

  7. Introduction to solitons

    Indian Academy of Sciences (India)

    Abstract. 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. 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.

  9. Optimal control of optical soliton parameters: Part 1. The Lax representation in the problem of soliton management

    International Nuclear Information System (INIS)

    Serkin, Vladimir N; Belyaeva, T L

    2001-01-01

    The existence of the Lax representation for a model of soliton management under certain conditions is shown, which proves a complete integrability of the model. The exact analytic solutions are obtained for the problem of the optimal control of parameters of Schrodinger solitons in nonconservative systems with the group velocity dispersion, nonlinear refractive index, and gain (absorption coefficient) varying over the length. The examples demonstrating the non-trivial amplification dynamics of optical solitons, which are important from practical point of view, are considered. The exact analytic solutions are obtained for problems of the optimal amplification of solitons in optical fibres with monotonically decreasing dispersion and of Raman pumping of solitons in fibreoptic communication systems. (solitons)

  10. Dark and bright solitons in a quasi-one-dimensional Bose-Einstein condensate

    International Nuclear Information System (INIS)

    Wang, Shun-Jin; Jia, Cheng-Long; An, Jun-Hong; Zhao, Dun; Luo, Hong-Gang

    2003-01-01

    The analytical dark and bright soliton solutions of the one-dimensional Gross-Pitaevskii equation with a confining potential are obtained. For the bright soliton, the recent experimental finding is studied, and the particle number of the soliton and the window of the particle numbers for the bright soliton to occur are estimated analytically and in good agreement with the experimental data. The existence of dark soliton for the attractive interaction and bright soliton for the repulsive interaction is predicted under proper conditions

  11. Three-Dimensional Hermite—Bessel—Gaussian Soliton Clusters in Strongly Nonlocal Media

    International Nuclear Information System (INIS)

    Jin Hai-Qin; Yi Lin; Liang Jian-Chu; Cai Ze-Bin; Liu Fei

    2012-01-01

    We analytically and numerically demonstrate the existence of Hermite—Bessel—Gaussian spatial soliton clusters in three-dimensional strongly nonlocal media. It is found that the soliton clusters display the vortex, dipole azimuthon and quadrupole azimuthon in geometry, and the total number of solitons in the necklaces depends on the quantum number n and m of the Hermite functions and generalized Bessel polynomials. The numerical simulation is basically identical to the analytical solution, and white noise does not lead to collapse of the soliton, which confirms the stability of the soliton waves. The theoretical predictions may give new insights into low-energetic spatial soliton transmission with high fidelity

  12. Analytical three-dimensional bright solitons and soliton pairs in Bose-Einstein condensates with time-space modulation

    International Nuclear Information System (INIS)

    Yan Zhenya; Hang Chao

    2009-01-01

    We provide analytical three-dimensional bright multisoliton solutions to the (3+1)-dimensional Gross-Pitaevskii equation with time- and space-dependent potential, time-dependent nonlinearity, and gain or loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

  13. Multicolor cavity soliton.

    Science.gov (United States)

    Luo, Rui; Liang, Hanxiao; Lin, Qiang

    2016-07-25

    We show a new class of complex solitary wave that exists in a nonlinear optical cavity with appropriate dispersion characteristics. The cavity soliton consists of multiple soliton-like spectro-temporal components that exhibit distinctive colors but coincide in time and share a common phase, formed together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor cavity soliton shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which would be very useful for 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.

  14. Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

    Science.gov (United States)

    Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

    2018-03-01

    We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

  15. Singularity confinement for maps with the Laurent property

    International Nuclear Information System (INIS)

    Hone, A.N.W.

    2007-01-01

    The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: The iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities

  16. Peaked and Smooth Solitons for K*(4,1 Equation

    Directory of Open Access Journals (Sweden)

    Yongan Xie

    2013-01-01

    Full Text Available This paper is contributed to explore all possible single peak solutions for the K*(4,1 equation ut=uxu2+2α(uuxxx+2uxuxx. Our procedure shows that the K*(4,1 equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1 equation.

  17. Solitons and rogue waves in spinor Bose-Einstein condensates

    Science.gov (United States)

    Li, Sitai; Prinari, Barbara; Biondini, Gino

    2018-02-01

    We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F =1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

  18. Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

    Science.gov (United States)

    Yue, Chen; Seadawy, Aly; Lu, Dianchen

    The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS) equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.

  19. Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

    Directory of Open Access Journals (Sweden)

    Chen Yue

    2016-01-01

    Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated.

  20. Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation

    Science.gov (United States)

    Zhang, Xiaoen; Chen, Yong

    2017-11-01

    In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.

  1. 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...... in a simple and general way the radiation of KdV and NS, as well as other types. of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the non-linearly self-trapped wave into the free-propagating radiation....

  2. Collisions of Two Spatial Solitons in Inhomogeneous Nonlinear Media

    International Nuclear Information System (INIS)

    Zhong Weiping; Yi Lin; Yang Zhengping; Xie Ruihua; Milivoj, Belic; Chen Goong

    2008-01-01

    Collisions of spatial solitons occurring in the nonlinear Schroeinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transverse dimension. In the self-focusing nonlinear media the spatial solitons can be transmitted stably, and the interaction between spatial solitons is enhanced due to the linear focusing effect (and also diminished for the linear defocusing effect). In the self-defocusing nonlinear media, in the absence of self-trapping or in the presence of linear self-defocusing, no transmission of stable spatial solitons is possible. However, in such media the linear focusing effect can be exactly compensated, and the spatial solitons can propagate through

  3. Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

    Science.gov (United States)

    Shtyrina, Olga V.; Fedoruk, Mikhail P.; Kivshar, Yuri S.; Turitsyn, Sergei K.

    2018-01-01

    We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization.

  4. The theory of singular perturbations

    CERN Document Server

    De Jager, E M

    1996-01-01

    The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

  5. Electro-magnetic waves within a model for charged solitons

    International Nuclear Information System (INIS)

    Borisyuk, Dmitry; Faber, Manfried; Kobushkin, Alexander

    2007-01-01

    We analyse the model of topological fermions (MTF), where charged fermions are treated as soliton solutions of the field equations. In the region far from the sources we find plane waves solutions with the properties of electro-magnetic waves

  6. Optical analogue of relativistic Dirac solitons in binary waveguide arrays

    Energy Technology Data Exchange (ETDEWEB)

    Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)

    2014-01-15

    We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.

  7. Potential motion for Thomas-Fermi non-topological solitons

    International Nuclear Information System (INIS)

    Bahcall, S.

    1992-04-01

    In the Thomas-Fermi approximation to theories of coupled fermions and scalars, the equations for spherically-symmetric non-topological solitons have the form of potential motion. This gives a straightforward method for proving the existence of non-topological solitons in a given theory and for finding the constant-density, saturating solutions

  8. Dynamics of coupled field solitons: A collective coordinate approach

    Indian Academy of Sciences (India)

    mensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate ... presented in some previous works [1,2] which where motivated by investigations intro- duced in [3,4], ... The collision of coupled field solitons leads to resonance structure depending on the energy ...

  9. Interaction between "dissipative solitons" stabilized by aggregation in excitable kinetics

    Science.gov (United States)

    Mangioni, Sergio E.

    2014-10-01

    We consider that a population of individuals governed by the Nagumo model is characterized by predisposition towards aggregation. "Dissipative solitons" interacting are solutions for such system. We changed the possibility of extinction, predicted by Nagumo model, by a uniform background of low population's density and then we observed relevant effect on interaction between "solitons".

  10. Effect of high-order dispersion on three-soliton interactions for the variable-coefficients Hirota equation.

    Science.gov (United States)

    Liu, Wenjun; Yang, Chunyu; Liu, Mengli; Yu, Weitian; Zhang, Yujia; Lei, Ming

    2017-10-01

    The interactions of multiple solitons show different properties with two-soliton interactions. For the difficulty of deriving multiple soliton solutions, it is rare to study multiple soliton interactions analytically. In this paper, three-soliton interactions in inhomogeneous optical fibers, which are described by the variable coefficient Hirota equation, are investigated. Via the Hirota bilinear method and symbolic computation, analytic three-soliton solutions are obtained. According to the obtained solutions, properties and features of three-soliton interactions are discussed by changing the third-order dispersion (TOD) and other relevant coefficients, and some plentiful structure of three-soliton interactions are presented for the first time. The influences of TOD on the intensity and propagation distance of solitons are described, which can be used to realize the soliton control. Besides, the method that can achieve the phase reverse of solitons is suggested, and bound states of three solitons are observed, which have potential applications in the mode-locked fiber lasers. Furthermore, comparing to two-soliton interactions, a novel phenomenon of three-soliton interactions with a strong phase shift at x=0 is revealed, which is potentially useful for optical logic switches.

  11. Adiabatic soliton laser.

    Science.gov (United States)

    Bednyakova, Anastasia; Turitsyn, Sergei K

    2015-03-20

    The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity-the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

  12. Pure-quartic solitons

    Science.gov (United States)

    Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad

    2016-01-01

    Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758

  13. Solitonic Josephson Thermal Transport

    Science.gov (United States)

    Guarcello, Claudio; Solinas, Paolo; Braggio, Alessandro; Giazotto, Francesco

    2018-03-01

    We explore the coherent thermal transport sustained by solitons through a long Josephson junction as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in conjunction with the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath=4.2 K . The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, whose positions can be externally controlled through a magnetic field and a bias current.

  14. Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

    Directory of Open Access Journals (Sweden)

    Xuemei Zhang

    2014-01-01

    Full Text Available This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt,  t∈0, 1;  x′0=0,  x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.

  15. Dynamical creation of complex vector solitons in spinor Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Xiong Bo; Gong Jiangbin

    2010-01-01

    By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.

  16. Higher-order-effects management of soliton interactions in the Hirota equation.

    Science.gov (United States)

    Wong, Pring; Liu, Wen-Jun; Huang, Long-Gang; Li, Yan-Qing; Pan, Nan; Lei, Ming

    2015-03-01

    The study of soliton interactions is of significance for improving pulse qualities in nonlinear optics. In this paper, interaction between two solitons, which is governed by the Hirota equation, is considered. Via use of the Hirota method, an analytic soliton solution is obtained. Then a two-period vibration phenomenon is observed. Moreover, turning points of the coefficients of higher-order terms, which are related with sudden delaying or leading, are found and analyzed. With different coefficient constraints, soliton interactions are discussed by different frequency separation with the split-step Fourier method, and characteristics of soliton interactions are exhibited. Through turning points, we get a pair of solitons which tend to be bound solitons but not exactly. Furthermore, we control a pair of solitons to emit at different emission angles. The stability of the two-period vibration is analyzed. Results in this paper may be helpful for the applications of optical self-routing, waveguiding, and faster switching.

  17. Phononless soliton waves as early forerunners of crystalline material fracture

    International Nuclear Information System (INIS)

    Dubovskij, O.A.; Orlov, A.V.

    2007-01-01

    Phononless soliton waves of compression are shown to generate at a critical tension of crystals featuring real Lennard-Jones potential of interatomic interaction just before their fracture. A new method of nonlinear micro dynamics was applied to define the initial atomic displacements at high excitation energies. A solution is found that corresponds to a soliton wave running before the front of fracture. In a bounded crystal, the soliton being reflected from the crystal boundary passes the front of fracture and deforms while moving in the opposite direction. The amplitude and spectral characteristics of that type of soliton waves in crystals with a modified Lennard-Jones potential have been investigated. An approximate analytical solution was found for the soliton waves [ru

  18. The analytical evolution of NLS solitons due to the numerical discretization error

    Science.gov (United States)

    Hoseini, S. M.; Marchant, T. R.

    2011-12-01

    Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t^{-{1\\over 2}}, which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank-Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found.

  19. The analytical evolution of NLS solitons due to the numerical discretization error

    International Nuclear Information System (INIS)

    Hoseini, S M; Marchant, T R

    2011-01-01

    Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank–Nicolson scheme and a scheme, due to Taha, based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t -1/2 , which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank–Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found. (paper)

  20. Multiple positive solutions of nonlinear singular m-point boundary value problem for second-order dynamic equations with sign changing coefficients on time scales

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2010-04-01

    \\end{array}\\right.$$ where $1\\leq k\\leq s\\leq m-2, a_i, b_i\\in(0,+\\infty$ with $0<\\sum_{i=1}^{k}b_{i}-\\sum_{i=k+1}^{s}b_{i}<1, 0<\\sum_{i=1}^{m-2}a_{i}<1, 0<\\xi_1<\\xi_2<\\cdots<\\xi_{m-2}<\\rho(T$, $f\\in C( [0,+\\infty,[0,+\\infty$, $a(t$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.

  1. Novel loop-like solitons for the generalized Vakhnenko equation

    International Nuclear Information System (INIS)

    Zhang Min; Ma Yu-Lan; Li Bang-Qing

    2013-01-01

    A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation

  2. Multi-hump bright solitons in a Schrödinger-mKdV system

    Science.gov (United States)

    Cisneros-Ake, Luis A.; Parra Prado, Hugo; López Villatoro, Diego Joselito; Carretero-González, R.

    2018-03-01

    We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg-de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS-mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.

  3. Quasiperiodic Envelope Solitons

    DEFF Research Database (Denmark)

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

    1999-01-01

    We analyze nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics. the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point...... out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally....

  4. Semirelativity and Kink Solitons

    Science.gov (United States)

    Nowak, Mariusz Karol

    2014-01-01

    It is hard to observe relativistic effects in everyday life. However, table experiments using a mechanical transmission line for solitons may be an efficient and simple way to show effects such as Lorentz contraction in a classroom. A kink soliton is a deformation of a lattice of several dozen or more pendulums placed on a wire and connected by a…

  5. Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

    Science.gov (United States)

    Li, Yu-E.; Xue, Ju-Kui

    2018-04-01

    We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

  6. Soliton synchronization in the focusing nonlinear Schrödinger equation.

    Science.gov (United States)

    Sun, Yu-Hao

    2016-05-01

    The focusing nonlinear Schrödinger equation (NLSE) describes propagation of quasimonochromatic waves in weakly nonlinear media. The aim of this study is to determine conditions of soliton synchronization in the NLSE in terms of the solitons' position and phase parameters. For this purpose, the concept of asymptotic middle states of solitons in the NLSE is first introduced. With soliton solutions of the NLSE, it is shown that soliton synchronization can be achieved by synchronizing the asymptotic middle states of the solitons, and conditions of soliton synchronization in terms of the solitons' position and phase parameters are given. Although the interaction of the solitons is nonlinear, the conditions are linear equations. Then, aided with the synchronization conditions, simple initial conditions are presented for producing synchronized interaction of solitons without the need to obtain analytic expressions for the synchronized interaction of the solitons. The initial conditions are summations of fundamental solitons with no mutual overlap, so they might be convenient to implement in applicative contexts.

  7. The cosmological singularity

    CERN Document Server

    Belinski, Vladimir

    2018-01-01

    Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...

  8. Characteristics of singularity-free static centrally symmetrical solutions of certain fourth-order gravitational-field equations

    Science.gov (United States)

    Fiedler, B.; Guenther, M.

    Fiedler and Schimming (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by Treder, admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = 0 (r radius), can now be extended to intervals 0 ≤ r ≤ α with arbitrarily large α.

  9. Bistable Helmholtz solitons in cubic-quintic materials

    International Nuclear Information System (INIS)

    Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

    2007-01-01

    We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations

  10. Gravitational collapse and naked singularities

    Indian Academy of Sciences (India)

    We propose the concept of 'effective naked singularities', which will be quite helpful ... If a pressure gradient force is not sufficiently strong, a body can continue collapsing due to its self-gravity. This phenomenon is called gravitational collapse. .... approaches a self-similar solution, which is called a critical solution, and then it.

  11. Vector solitons for the reduced Maxwell-Bloch equations with variable coefficients in nonlinear optics

    Science.gov (United States)

    Chai, Jun; Tian, Bo; Sun, Wen-Rong; Liu, De-Yin

    2018-01-01

    Under investigation in this paper is the reduced Maxwell-Bloch equations with variable coefficients, which describe the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Hirota method and symbolic computation are applied to solve such equations. By introducing the dependent variable transformations, we give the bilinear forms, vector one-, two- and N-soliton solutions in analytic forms. The types of the vector solitons are analyzed: Only the bright-single-hump solitons can be observed in q and r1 , the soliton in r2 is the bright-double-hump soliton, and there exist three types of solitons in r3 , including the dark-single-hump soliton, dark-double-hump soliton and dark-like-bright soliton, with q as the inhomogeneous electric field, r1 and r2 as the real and imaginary parts of the polarization of the two-level medium, and r3 as the population difference between the ground and excited states. Figures are presented to show the vector soliton solutions. Different types of the interactions between the vector two solitons are presented. In each component, only the overtaking elastic interaction can be observed.

  12. Analytical identification of soliton dynamics in normal-dispersion passively mode-locked fiber lasers: from dissipative soliton to dissipative soliton resonance.

    Science.gov (United States)

    Lin, Wei; Wang, Simin; Xu, Shanhui; Luo, Zhi-Chao; Yang, Zhongmin

    2015-06-01

    A combined analytical approach to classify soliton dynamics from dissipative soliton to dissipative soliton resonance (DSR) is developed based on the established laser models. The approach, derived from two compatible analytical solutions to the complex cubic-quintic Ginzburg-Landau equation (CQGLE), characterizes the pulse evolution process from both algebraic and physical points of view. The proposed theory is proved to be valid in real world laser oscillators according to numerical simulations, and potentially offers guideline on the design of DSR cavity configurations.

  13. soliton dynamics in a modified Yakushevich model

    Indian Academy of Sciences (India)

    1Department of Physics, College of Engineering and Technology, Biju Patnaik University of Technology, Bhubaneswar 751 ... senting different bases and find two new in-phase solitonic solutions. We also discuss here the effect of ..... (29) and adoption of the procedure of linear perturbation anal- ysis [13-15] gives. ШШ =.

  14. Solitons in Bose–Einstein condensates

    Indian Academy of Sciences (India)

    The solution (8) shows that both the density profile ρ(z) and the phase profile φ(z) travel with the same speed ... always travel with different speeds, contrary to the solitons of the repulsive GPE, where they travel with the ... tory using standing waves of laser light, load BEC atoms on such lattices, and also tune the interactions ...

  15. Quantization of bag-like solitons

    International Nuclear Information System (INIS)

    Breit, J.D.

    1982-01-01

    The method of collective coordinates is used to quantize bag-like solitons formed by scalar and spinor fields. This method leads to approximate wave functions for quarks in the bag that are orthogonal to the translational modes. Solutions are given for the MIT bag limit of the fields. (orig.)

  16. Strings, Axions and Solitons.

    Science.gov (United States)

    Dabholkar, Atish

    This thesis is divided into two chapters. Chapter I is about the dynamics of radiating axionic strings and the lower bound on the mass of the invisible axion. It has been suggested that, without inflation, the decay of axionic strings produced after the Peccei -Quinn phase transition is the primary source of cosmic relic axions. Knowing the density of these axions would then allow the derivation of a cosmological bound on the mass of the axion. In order to obtain a sharp bound it is essential to know the spectrum of the emitted axions and the detailed motion of a global string strongly coupled to the axionic field. To this end, following the analogy with Dirac's treatment of classical radiating electrons, self-consistent renormalized equations are obtained that describe the dynamics of a radiating global string interacting with its surrounding axionic field. The numerical formalism for evolving string trajectories using these equations is described, and is applied to the case of a circular loop. It is argued that for large wavelength oscillations of cosmic string loops, the motion is well approximated by the motion of a free Nambu-Goto string with appropriate renormalization. Consequently, a lower bound of 10 ^{-3} eV on the mass of the axion is obtained. Together with the recent upperbound of 4 times 10^{-4 } eV from the supernova SN1987a, it marginally rules out the invisible axion. Chapter II is about superstrings and solitons. It is shown that the quantum renormalization of the superstring tension vanishes to all orders in string perturbation theory. A low-energy analysis of macroscopic superstrings is presented and various analogies between these superstrings and solitons in supersymmetric theories are discussed. These include the existence of exact multi-string solutions of the low -energy supergravity super-Yang-Mills equations of motion and a Bogomol'nyi bound for the energy per unit length which is saturated by these solutions. Arguments are presented that

  17. Dissipative solitons in pair-ion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Ghosh, Samiran, E-mail: sran-g@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India)

    2014-01-15

    The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.

  18. Bright and dark solitons in optical fibers with parabolic law nonlinearity

    Directory of Open Access Journals (Sweden)

    Milović Daniela

    2013-01-01

    Full Text Available This paper utilizes the ansatz method to obtain bright and dark 1-soliton solution to the nonlinear Schrodinger’s equation with parabolic law nonlinearity in birefringent fibers. There are a few Hamiltonian type perturbation terms taken into account. The exact soliton solution comes with baggages that are referred to as constraint conditions that must hold in order for these solitons to exist.

  19. Helmholtz algebraic solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2010-01-01

    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.

  20. Fuzzy Objects and Noncommutative Solitons

    Science.gov (United States)

    Kobayashi, Shinpei; Asakawa, Tsuguhiko

    2015-01-01

    The fuzzy disc is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. We showed that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We also constructed fan-shaped soliton solutions, which would be identified with D-branes, of a scalar field theory on the fuzzy disc and applied this concept to a theory of noncommutative gravity. This proceeding is based on our previous work.

  1. Observation of Kuznetsov-Ma soliton dynamics in optical fibre

    Science.gov (United States)

    Kibler, B.; Fatome, J.; Finot, C.; Millot, G.; Genty, G.; Wetzel, B.; Akhmediev, N.; Dias, F.; Dudley, J. M.

    2012-01-01

    The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, although the first solution of this type was the Kuznetzov-Ma (KM) soliton derived in 1977, there have in fact been no quantitative experiments confirming its validity. We report here novel experiments in optical fibre that confirm the KM soliton theory, completing an important series of experiments that have now observed a complete family of soliton on background solutions to the NLSE. Our results also show that KM dynamics appear more universally than for the specific conditions originally considered, and can be interpreted as an analytic description of Fermi-Pasta-Ulam recurrence in NLSE propagation. PMID:22712052

  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....

  3. Solitons and confinement

    International Nuclear Information System (INIS)

    Swieca, J.A.

    1976-01-01

    Some aspects of two recent developments in quantum field theory are discussed. First, related with 'extended particles' such as soliton, kink and the 't Hooft monopole. Second, with confinement of particles which are realized in the Schwinger model [pt

  4. The Baryon Number Two System in the Chiral Soliton Model

    International Nuclear Information System (INIS)

    Mantovani-Sarti, V.; Drago, A.; Vento, V.; Park, B.-Y.

    2013-01-01

    We study the interaction between two B = 1 states in a chiral soliton model where baryons are described as non-topological solitons. By using the hedgehog solution for the B = 1 states we construct three possible B = 2 configurations to analyze the role of the relative orientation of the hedgehog quills in the dynamics. The strong dependence of the inter soliton interaction on these relative orientations reveals that studies of dense hadronic matter using this model should take into account their implications. (author)

  5. Breaking soliton equations and negative-order breaking soliton ...

    Indian Academy of Sciences (India)

    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 ...

  6. Brane singularities and their avoidance

    International Nuclear Information System (INIS)

    Antoniadis, Ignatios; Cotsakis, Spiros; Klaoudatou, Ifigeneia

    2010-01-01

    The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state P = γρ between the 'pressure' P and the 'density' ρ, our results depend crucially on the constant fluid parameter γ. (i) For γ > -1/2, the flat brane solution suffers from a collapse singularity at a finite distance that disappears in the curved case. (ii) For γ < -1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1 < γ ≤ -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.

  7. Spectral analysis for differential operators with singularities

    Directory of Open Access Journals (Sweden)

    Vjacheslav Anatoljevich Yurko

    2004-01-01

    Full Text Available Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigen- and associated functions, and investigate the inverse problem of recovering the boundary value problem from its spectral characteristics.

  8. Singularities in the nonisotropic Boltzmann equation

    International Nuclear Information System (INIS)

    Garibotti, C.R.; Martiarena, M.L.; Zanette, D.

    1987-09-01

    We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs

  9. On the genericity of spacetime singularities

    Indian Academy of Sciences (India)

    in terms of the incompleteness of non-space-like geodesics in spacetime. It is possible that such ... outside. The above discussion does not imply the absence of singularity-free solutions to Einstein's equations. ..... spherical collapse also turns out to be a stable feature as implied by the singularity theorems discussed above.

  10. Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.

    Science.gov (United States)

    Dai, Chaoqing; Wang, Yueyue; Zhang, Xiaofei

    2014-12-01

    The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.

  11. Bistable dark solitons of a cubic-quintic Helmholtz equation

    International Nuclear Information System (INIS)

    Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.

    2010-01-01

    We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.

  12. Stability of nonlinear ion sound waves and solitons in plasmas

    International Nuclear Information System (INIS)

    Infeld, E.; Rowlands, G.

    1979-01-01

    Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the Korteweg-de Vries equation, which gives stability for non linear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5 A three-dimensional generalization of the Korteweg-de Vries equation is considered but this leads to stability for all non linear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit. (author)

  13. The geometry of warped product singularities

    Science.gov (United States)

    Stoica, Ovidiu Cristinel

    In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

  14. Naked singularity, firewall, and Hawking radiation.

    Science.gov (United States)

    Zhang, Hongsheng

    2017-06-21

    Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

  15. Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

    Science.gov (United States)

    Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

    2017-10-01

    Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

  16. 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.

  17. 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.

  18. The volume of a soliton

    International Nuclear Information System (INIS)

    Adam, C.; Haberichter, M.; Wereszczynski, A.

    2016-01-01

    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.

  19. Noncommuting Momenta of Topological Solitons

    Science.gov (United States)

    Watanabe, Haruki; Murayama, Hitoshi

    2014-05-01

    We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

  20. Nonlinear compression of optical solitons

    Indian Academy of Sciences (India)

    pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects. Keywords. Optical solitons; bright and dark solitons; nonlinear compression; phase modulation; fibre amplification; loss. PACS Nos 42.81. Dp; 02.30 Jr; 04.30 Nk. 1. Introduction. The term soliton refers to special kinds of waves that ...

  1. Multiple soliton production and the Korteweg-de Vries equation.

    Science.gov (United States)

    Hershkowitz, N.; Romesser, T.; Montgomery, D.

    1972-01-01

    Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

  2. On the reflection of solitons of the cubic nonlinear Schrödinger equation

    KAUST Repository

    Katsaounis, Theodoros

    2016-07-05

    In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.

  3. Bose gas with two- and three-particle interaction: evolution of soliton-like bubbles

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Kholmurodov, Kh.T.

    1988-01-01

    Solutions of the non-linear Schroedinger equation (NSE) for the Bose gas with two- and three-particle interaction are considered. Problems of soliton-like bubble existence, stability and evolution of the moving soliton are studied. It is shown that at D=2.3 for low-amplitude waves propagating at the transonic velocity the NSE is reduced to a two- and three-dimensional Kadomtsev-Petviashvili (KP) equation and the NSE bubble soliton transfers to the KP one

  4. Bright Solitons in a PT-Symmetric Chain of Dimers

    Directory of Open Access Journals (Sweden)

    Omar B. Kirikchi

    2016-01-01

    Full Text Available We study the existence and stability of fundamental bright discrete solitons in a parity-time- (PT- symmetric coupler composed by a chain of dimers that is modelled by linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms. We use a perturbation theory for small coupling between the lattices to perform the analysis, which is then confirmed by numerical calculations. Such analysis is based on the concept of the so-called anticontinuum limit approach. We consider the fundamental onsite and intersite bright solitons. Each solution has symmetric and antisymmetric configurations between the arms. The stability of the solutions is then determined by solving the corresponding eigenvalue problem. We obtain that both symmetric and antisymmetric onsite mode can be stable for small coupling, in contrast to the reported continuum limit where the antisymmetric solutions are always unstable. The instability is either due to the internal modes crossing the origin or the appearance of a quartet of complex eigenvalues. In general, the gain-loss term can be considered parasitic as it reduces the stability region of the onsite solitons. Additionally, we analyse the dynamic behaviour of the onsite and intersite solitons when unstable, where typically it is either in the form of travelling solitons or soliton blow-ups.

  5. Head on collision of multi-solitons in an electron-positron-ion plasma having superthermal electrons

    Energy Technology Data Exchange (ETDEWEB)

    Roy, Kaushik, E-mail: kaushikbolpur@rediffmail.com [Beluti M. K. M. High School, P.O. Beluti, Birbhum, West Bengal 731301 (India); Chatterjee, Prasanta, E-mail: prasantachatterjee1@rediffmail.com; Roychoudhury, Rajkumar [Department of Mathematics, Siksha Bhavana Visva Bharati, Santiniketan 731235 (India)

    2014-10-15

    The head-on collision and overtaking collision of four solitons in a plasma comprising superthermal electrons, cold ions, and Boltzmann distributed positrons are investigated using the extended Poincare-Lighthill-Kuo (PLK) together with Hirota's method. PLK method yields two separate Korteweg-de Vries (KdV) equations where solitons obtained from any KdV equation move along a direction opposite to that of solitons obtained from the other KdV equation, While Hirota's method gives multi-soliton solution for each KdV equation all of which move along the same direction where the fastest moving soliton eventually overtakes the other ones. We have considered here two soliton solutions obtained from Hirota's method. Phase shifts acquired by each soliton due to both head-on collision and overtaking collision are calculated analytically.

  6. Productivity Formulae of an Infinite-Conductivity Hydraulically Fractured Well Producing at Constant Wellbore Pressure Based on Numerical Solutions of a Weakly Singular Integral Equation of the First Kind

    Directory of Open Access Journals (Sweden)

    Chaolang Hu

    2012-01-01

    Full Text Available In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these two methods are in accordance with each other. And then the solutions of the weakly singular integral equation are utilized for the productivity formula of hydraulic fractured wells producing at constant pressure, which provide fast analytical tools to evaluate production performance of infinite-conductivity fractured wells. The paper also shows equipotential threads, which are generated from the numerical results, with different fluid potential values. These threads can be approximately taken as a family of ellipses whose focuses are the two endpoints of the fracture, which is in accordance with the regular assumption in Kuchuk and Brigham, 1979.

  7. Soliton driven angiogenesis.

    Science.gov (United States)

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

    2016-08-09

    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.

  8. Klasifikasi Interaksi Gelombang Permukaan Bertipe Dua Soliton

    OpenAIRE

    sutimin, Sutimin; Rusgiyono, Agus

    2001-01-01

    Pada tulisan ini diselidiki, masalah klasifikasi interaksi gelombang bertipe dua soliton Kadomtsev-Petviashvilli (KP). Disini dianalisis berdasarkan parameter interaksi dua solusi soliton baik melalui harga eksak maupun proses pelimitan. Proses pelimitan ini dilakukan untuk mengetahui resonansi diantara dua soliton. Selanjutnya resonansi soliton ini dikaji untuk mendapatkan soliton yang baru.

  9. Soliton equations solved by the boundary CFT

    OpenAIRE

    Saito, Satoru; Sato, Ryuichi

    2003-01-01

    Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under the influence of the boundary is calculated explicitly and is shown that it is frozen at the Dirichlet limit.

  10. Direct soliton generation in microresonators.

    Science.gov (United States)

    Bao, Chengying; Xuan, Yi; Jaramillo-Villegas, Jose A; Leaird, Daniel E; Qi, Minghao; Weiner, Andrew M

    2017-07-01

    We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.

  11. Solitons and particles

    National Research Council Canada - National Science Library

    Rebbi, Claudio; Soliani, G

    1984-01-01

    ... may find in the reprints on the mathematical theories of solitons useful ideas and inspirations, while the latter may find in this volume interesting and challenging applications of the concept of solitons in the domain of particle physics. We would like to express our gratitude to the many colleagues, in particular to Sidney Coleman, Neil Craigie, Roman Jackiw and Ed Witten, who have given us advice in the selection of the reprints. We are also thankful to Dr. Phua and World Scientific Publishing Co. for giving u...

  12. New exact traveling wave solutions to the (1+1-dimensional Klein-Gordon-Zakharov equation for wave propagation in plasma using the exp(-Φ(ξ-expansion method

    Directory of Open Access Journals (Sweden)

    M.G. Hafez

    2015-03-01

    Full Text Available The (1+1-dimensional nonlinear Klein-Gordon-Zakharov equation considered as a model equation for describing the interaction of the Langmuir wave and the ion acoustic wave in high frequency plasma. By the execution of the exp(-Φ(ξ-expansion, we obtain new explicit and exact traveling wave solutions to this equation. The obtained solutions include kink, singular kink, periodic wave solutions, soliton solutions and solitary wave solutions of bell types. The variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in plasma physics and engineering.

  13. Bifurcations of traveling wave solutions for an integrable equation

    International Nuclear Information System (INIS)

    Li Jibin; Qiao Zhijun

    2010-01-01

    This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.

  14. Interactions of Soliton Waves for a Generalized Discrete KdV Equation

    International Nuclear Information System (INIS)

    Zhou Tong; Zhu Zuo-Nong

    2017-01-01

    It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. (paper)

  15. Stability of line solitons for the KP-II equation in R2

    CERN Document Server

    Mizumachi, Tetsu

    2015-01-01

    The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x\\to\\infty. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=\\pm\\infty. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

  16. Nonlinear de Broglie waves and the relation between relativistic and nonrelativistic solitons

    International Nuclear Information System (INIS)

    Barut, A.O.; Baby, B.V.

    1988-07-01

    It is shown that the well-known envelope soliton and kink solutions of the nonlinear Schroedinger equation are the nonrelativistic limit of the corresponding solutions of the nonlinear Klein-Gordon equation. 34 refs

  17. Self-trapped optical beams: Spatial solitons

    Indian Academy of Sciences (India)

    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.

  18. Spatiotemporal optical solitons

    International Nuclear Information System (INIS)

    Malomed, Boris A; Mihalache, Dumitru; Wise, Frank; Torner, Lluis

    2005-01-01

    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)

  19. The nontopological soliton model

    International Nuclear Information System (INIS)

    Wilets, L.

    1988-01-01

    The nontopological soliton model introduced by Friedberg and Lee, and variations of it, provide a method for modeling QCD which can effectively include the dynamics of hadronic collisions as well as spectra. Absolute color confinement is effected by the assumed dielectric properties of the medium. A recently proposed version of the model is chirally invariant. 32 refs., 5 figs., 1 tab

  20. Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations.

    Science.gov (United States)

    Chowdury, Amdad; Krolikowski, Wieslaw

    2017-06-01

    We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.

  1. Soliton interaction as a possible model for extreme waves in shallow water

    NARCIS (Netherlands)

    Peterson, P.; Soomere, T.; Engelbrecht, J.; van Groesen, Embrecht W.C.

    2003-01-01

    Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area

  2. Interaction of spatial photorefractive solitons

    DEFF Research Database (Denmark)

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

    1998-01-01

    We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solita...... 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.......We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solitary...

  3. The Geometry of Black Hole Singularities

    Directory of Open Access Journals (Sweden)

    Ovidiu Cristinel Stoica

    2014-01-01

    Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

  4. Stability of matter-wave solitons in optical lattices

    Science.gov (United States)

    Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

    2010-08-01

    We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

  5. Many-body interaction in fast soliton collisions.

    Science.gov (United States)

    Peleg, Avner; Nguyen, Quan M; Glenn, Paul

    2014-04-01

    We study n-pulse interaction in fast collisions of N solitons of the cubic nonlinear Schrödinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a generalized reduced model that yields the contribution of the n-pulse interaction to the amplitude shift for collisions in the presence of weak (2m+1)-order loss, for any n and m. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss (m=3). Our calculations show that the three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form G(|ψ|2)ψ, where ψ is the physical field and G is a Taylor polynomial of degree mc. Considering mc=3, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that n-pulse interaction with high n values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of n-pulse interaction effects with n and m and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from that observed in fast NLS soliton collisions in the presence of cubic loss.

  6. Traveling solitons in Lorentz and CPT breaking systems

    International Nuclear Information System (INIS)

    Souza Dutra, A. de; Correa, R. A. C.

    2011-01-01

    In this work we present a class of traveling solitons in Lorentz and CPT breaking systems. In the case of Lorentz violating scenarios, as far as we know, only static solitonic configurations were analyzed up to now in the literature. Here it is shown that it is possible to construct some traveling solitons which cannot be mapped into static configurations by means of Lorentz boosts due to explicit breaking. In fact, the traveling solutions cannot be reached from the static ones by using something similar to a Lorentz boost in those cases. Furthermore, in the model studied, a complete set of exact solutions is obtained. The solutions present a critical behavior controlled by the choice of an arbitrary integration constant.

  7. The volume of a soliton

    Directory of Open Access Journals (Sweden)

    C. Adam

    2016-03-01

    Full Text Available 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.

  8. Chiral solitons a review volume

    CERN Document Server

    1987-01-01

    This review volume on topological and nontopological chiral solitons presents a global view on the current developments of this field in particle and nuclear physics. The book addresses problems in quantization, restoration of translational and rotational symmetry, and the field theoretical approach to solitons which are common problems in the field of solitons. Primarily aimed for graduate students and the novice in the field, the collected articless cover a broad spectrum of topics in formalism as well as phenomenology.

  9. Capture and confinement of solitons in nonlinear integrable systems

    International Nuclear Information System (INIS)

    Mel'nikov, V.K.

    1988-01-01

    Some nonlinear integrable systems were found to have solutions describing solitons that come from infinity and then are captured into oscillatory regimes. These solutions were obtained by the inverse scattering method for the one-dimensional Schroedinger operator on a straight line. The obtained results are relevant to some problems of hydrodynamics, plasma physics, solid state physics, etc. 2 refs

  10. Collisional Effect On Magnetosonic Solitons In A Dusty Plasma Slab ...

    African Journals Online (AJOL)

    An analytical investigation of collisional effect on magnetosonic solitons in a dusty plasma slab is presented. We have derived and presented solutions of nonlinear magetohydrodynamic equations for a warm dusty magnetoplasma. It is observed that, our work could be considered a general case for magnetosonic solutions ...

  11. One-parameter family of solitons from minimal surfaces

    Indian Academy of Sciences (India)

    In this paper, we discuss a one parameter family of complex Born–Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B–I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples.

  12. One-parameter family of solitons from minimal surfaces

    Indian Academy of Sciences (India)

    Abstract. In this paper, we discuss a one parameter family of complex Born–Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B–I equation from a given complex solution of a special type (which are abundant). We illustrate this with many ...

  13. Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system.

    Science.gov (United States)

    Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

    2018-01-01

    General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

  14. Biological soliton in multicellular movement

    Science.gov (United States)

    Kuwayama, Hidekazu; Ishida, Shuji

    2013-01-01

    Solitons have been observed in various physical phenomena. Here, we show that the distinct characteristics of solitons are present in the mass cell movement of non-chemotactic mutants of the cellular slime mould Dictyostelium discoideum. During starvation, D. discoideum forms multicellular structures that differentiate into spore or stalk cells and, eventually, a fruiting body. Non-chemotactic mutant cells do not form multicellular structures; however, they do undergo mass cell movement in the form of a pulsatile soliton-like structure (SLS). We also found that SLS induction is mediated by adhesive cell-cell interactions. These observations provide novel insights into the mechanisms of biological solitons in multicellular movement. PMID:23893301

  15. Existence of a solution to the Dirichlet problem associated to a second-order differential equation with singularities: the method of lower and upper functions

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2013-01-01

    Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030. xml ?format=INT

  16. Existence of a solution to the Dirichlet problem associated to a second-order differential equation with singularities: the method of lower and upper functions

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2013-01-01

    Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030.xml?format=INT

  17. Non-topological soliton bag model

    International Nuclear Information System (INIS)

    Wilets, L.

    1986-01-01

    The Friedberg-Lee soliton model, which effects confinement by a quantal scalar field, is discussed. The Lagrangian for the non-topological soliton model is the usual QCD Lagrangian supplemented by a non-linear scalar sigma field term. Static solutions to the field equations are considered in the mean field approximation. Small amplitude oscillations are discussed. Quantum alternatives to the mean field approximation are also considered. Methods of momentum projection and Lorentz boost are described, and the generator coordinate method is discussed. Calculations of the N-N interaction are reviewed briefly. Also discussed is one-gluon exchange, as well as the pion and dressing of the baryons. The hadron states are summarized. One loop quantum corrections are discussed briefly. Work in progress is mentioned in the areas of N-anti N annihilation, the many bag problem, and a Pauli equation for the nucleon. 31 refs

  18. Finite conformal quantum gravity and spacetime singularities

    Science.gov (United States)

    Modesto, Leonardo; Rachwał, Lesław

    2017-12-01

    We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

  19. Geodesic fields with singularities

    International Nuclear Information System (INIS)

    Kafker, A.H.

    1979-01-01

    The question considered is whether or not a Riemannian metric can be found to make a given curve field on a closed surface into geodesics. Allowing singularities removes the restriction to Euler characteristic zero. The main results are the following: only two types of isolated singularities can occur in a geodesic field on a surface. No geodsic fields exist on a surface with Euler characteristic less than zero. If the Euler characteristic is zero, such a geodesic field can have only removable singularities. Only a limited number of geodesic fields exist on S 2 and RP 2 . A closed geodesic (perhaps made from several curves and singularities) always appears in such a field

  20. Asymmetric spatial soliton dragging.

    Science.gov (United States)

    Blair, S; Wagner, K; McLeod, R

    1994-12-01

    A new low-latency, cascadable optical logic gate with gain, high contrast, and three-terminal input-output isolation is introduced. The interaction between two orthogonally polarized spatial solitons brought into coincidence at the boundary of a saturating nonlinear medium and propagating in different directions results in the phase-insensitive spatial dragging of a strong pump soliton by a weaker signal. As a result, the strong pump is transmitted through an aperture when the weak signal is not present, and it is dragged to the side by more than a beam width and blocked in the presence of the weak signal, thus implementing an inverter with gain. A multi-input, logically complete NOR gate also can be implemented in a cascaded system.

  1. Geometric Singularities of the Stokes Problem

    Directory of Open Access Journals (Sweden)

    Nejmeddine Chorfi

    2014-01-01

    Full Text Available When the domain is a polygon of ℝ2, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.

  2. Breaking soliton equations and negative-order breaking soliton ...

    Indian Academy of Sciences (India)

    2016-10-06

    Oct 6, 2016 ... Abstract. 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 distinct dispersion relation for each equation. We use the simplified Hirota's method to ...

  3. Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity

    Energy Technology Data Exchange (ETDEWEB)

    Ponglertsakul, Supakchai, E-mail: supakchai.p@gmail.com; Winstanley, Elizabeth, E-mail: E.Winstanley@sheffield.ac.uk

    2017-01-10

    We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.

  4. Isotopy of Morin singularities

    OpenAIRE

    Saji, Kentaro

    2015-01-01

    We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.

  5. Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

    KAUST Repository

    Crosta, M.

    2011-12-05

    We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.

  6. On combined optical solitons of the one-dimensional Schrödinger’s equation with time dependent coefficients

    Directory of Open Access Journals (Sweden)

    Kilic Bulent

    2016-01-01

    Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.

  7. Quantum propagation across cosmological singularities

    Science.gov (United States)

    Gielen, Steffen; Turok, Neil

    2017-05-01

    The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

  8. Oscillating solitons in nonlinear optics

    Indian Academy of Sciences (India)

    ... 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.

  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...

  10. Gravitational field of Schwarzschild soliton

    Directory of Open Access Journals (Sweden)

    Musavvir Ali

    2015-01-01

    Full Text Available The aim of this paper is to study the gravitational field of Schwarzschild soliton. Use of characteristic of λ-tensor is given to determine the kinds of gravitational fields. Through the cases of two and three dimension for Schwarzschild soliton, the Gaussian curvature is expressed in terms of eigen values of the characteristic equation.

  11. Introduction to singularities

    CERN Document Server

    Ishii, Shihoko

    2014-01-01

    This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundar...

  12. Singularities formation, structure, and propagation

    CERN Document Server

    Eggers, J

    2015-01-01

    Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

  13. Breather soliton dynamics in microresonators

    Science.gov (United States)

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

    2017-01-01

    The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that 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, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. 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. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science. PMID:28232720

  14. Soliton mobility in disordered lattices.

    Science.gov (United States)

    Sun, Zhi-Yuan; Fishman, Shmuel; Soffer, Avy

    2015-10-01

    We investigate soliton mobility in the disordered Ablowitz-Ladik (AL) model and the standard nonlinear Schrödinger (NLS) lattice with the help of an effective potential generalizing the Peierls-Nabarro potential. This potential results from a deviation from integrability, which is due to randomness for the AL model, and both randomness and lattice discreteness for the NLS lattice. The statistical properties of such a potential are analyzed, and it is shown how the soliton mobility is affected by its size. The usefulness of this effective potential in studying soliton dynamics is demonstrated numerically. Furthermore, we propose two ways to enhance soliton transport in the presence of disorder: one is to use specific realizations of randomness, and the other is to consider a specific soliton pair.

  15. String theory and cosmological singularities

    Indian Academy of Sciences (India)

    time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities ...

  16. 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.

  17. 'Footballs', conical singularities, and the Liouville equation

    International Nuclear Information System (INIS)

    Redi, Michele

    2005-01-01

    We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints

  18. Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework.

    Science.gov (United States)

    Slunyaev, A V; Pelinovsky, E N

    2016-11-18

    The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

  19. Nonlinear singularly perturbed optimal control problems with singular arcs. [flight mechanics application

    Science.gov (United States)

    Ardema, M. D.

    1979-01-01

    Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

  20. The nonlinear Fourier analysis of internal solitons in the Andaman sea

    International Nuclear Information System (INIS)

    Osborne, A.R.; Provenzale, A.; Bergamasco, L.

    1983-01-01

    A preliminary spectral analysis of large-amplitude internal solitons in the Andaman Sea was conducted, employing method based upon the spectral (or scattering) transform solution of the Korteweg-de Vries equation

  1. Variational methods in nonlinear field equations solitary waves, hylomorphic solitons and vortices

    CERN Document Server

    Benci, Vieri

    2014-01-01

    The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.

  2. Scalar-vector soliton fiber laser mode-locked by nonlinear polarization rotation.

    Science.gov (United States)

    Wu, Zhichao; Liu, Deming; Fu, Songnian; Li, Lei; Tang, Ming; Zhao, Luming

    2016-08-08

    We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.

  3. Nonlinear waves and solitons propagating perpendicular to the magnetic field in bi-ion plasma with finite plasma pressure

    Directory of Open Access Journals (Sweden)

    E. M. Dubinin

    2002-01-01

    Full Text Available We investigate the nature of nonlinear waves propagating transverse to the magnetic field in a bi-ion plasma including plasma pressure. By using the conservation laws derived from the multi-ion fluid equations the system may be described by a single order differential equation whose properties control the structure of the flow and the magnetic field. Compressive solitons exist in specific ranges of the characteristic Mach numbers. Various features of solitons differ in different existence "windows". For example, there are solitons that contain a strong proton rarefaction core embedded in the main compressional structure. Compressive solitons are found in a wide range of flow parameters. Finite ion pressure introduces critical Mach numbers. In contrast to a plasma consisting only of protons and electrons these singular points are reached where a specific combination of ion and electron speeds lies on particular locii, in multi-parameter space, which corresponds to the generalized "sonic point" of the compound system.

  4. Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

    Science.gov (United States)

    Trofimov, Vyacheslav A.; Lysak, Tatiana M.

    2018-04-01

    We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

  5. 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

  6. Noise induced creation and annihilation of solitons in dispersion managed fiber oscillators

    Science.gov (United States)

    Teamir, Tesfay G.; Ilday, F. Ömer

    2017-01-01

    Optical solitons and their interaction with other solitons or with dispersive wave shed by solitons under perturbation constitute a versatile experimental and theoretical platform for studying the nature of complex dynamics occurring in laser cavities [1-3] in addition to common physical principles in terms with a range of other nonlinear, non-equilibrium, coupled systems outside of optics. A soliton is energy localization of dissipative structures of electric field which evolves from noise in laser cavities. It is stationary solution of nonlinear Schrödinger equation that balances the effects of chromatic dispersion with nonlinearity during propagation in a medium. Strong pumping in soliton regime drives a laser system in to a multi pulsing self-organized system. Such a system in fiber medium is ubiquitous and always attracts research interest. Multi-soliton pulses or soliton bunches generated from different systems through a long range interaction due to acoustic waves generated from electrostriction and its perturbation induced refractive index change of the medium by a propagating pulse on the next pulse in the neighborhood. A short range interaction can occur as a result of pulses overlapping, acoustoptic interaction or it can occur when dispersive waves at the tail of pulses interact with a back ground field or with solitons near to its.

  7. Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side

    Science.gov (United States)

    Amirjanyan, A. A.; Sahakyan, A. V.

    2017-08-01

    A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.

  8. Observation of Coexisting Dissipative Solitons in a Mode-Locked Fiber Laser.

    Science.gov (United States)

    Bao, Chengying; Chang, Wonkeun; Yang, Changxi; Akhmediev, Nail; Cundiff, Steven T

    2015-12-18

    We show, experimentally and numerically, that a mode-locked fiber laser can operate in a regime where two dissipative soliton solutions coexist and the laser will periodically switch between the solutions. The two dissipative solitons differ in their pulse energy and spectrum. The switching can be controlled by an external perturbation and triggered even when switching does not occur spontaneously. Numerical simulations unveil the importance of the double-minima loss spectrum and nonlinear gain to the switching dynamics.

  9. Tanh-type and sech-type solitons for some space-time fractional PDE models

    Science.gov (United States)

    Guner, Ozkan; Bekir, Ahmet; Korkmaz, Alper

    2017-02-01

    Tanh-type and sech-type soliton solutions are constructed for the fractional modified KdV-Zakharov-Kuznetsov equation and the fractional generalized Duffing equation. Both equations are reduced to ordinary differential equations by using compatible fractional complex transforms. Suitable powers of tanh and sech ansatzs including unknown free parameters are applied to both equations. After determining the powers, these parameters are determined using computer algebra. The obtained soliton solutions are depicted for particular cases for various values of derivative order.

  10. Modulational instability, solitons and periodic waves in a model of quantum degenerate boson-fermion mixtures

    International Nuclear Information System (INIS)

    Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym

    2007-01-01

    In this paper, we study a system of coupled nonlinear Schroedinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and write explicit solutions in the form of periodic waves. We also check that the solitons observed previously in numerical simulations of the model correspond exactly to our explicit solutions and see how plane waves destabilize to form periodic waves

  11. Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods

    Directory of Open Access Journals (Sweden)

    Dianchen Lu

    Full Text Available In this article, we study one of the most popular models in nature and also industrial which is the van der Waals normal form for the fluidized granular matter. Understanding of static and dynamic property for these kinds of the models is very important in many aspects of industrial from pharmaceuticals to civil engineering and also some basic physical phenomena like those studied in geophysics. This model explains the phase separation phenomenon. We apply six different methods for this model to obtained the traveling and solitary wave solutions. We make the comparison between obtained solutions with each of them and also with obtained solutions with different methods. Keywords: The van der Waals normal form for fluidized granular matter, Modified simple equation method, The improved mapping approach and variable separation method, Traveling wave solutions, Solitary wave solutions, Mathematical physics

  12. Shock bifurcation and emergence of diffusive solitons in a nonlinear wave equation with relaxation

    Energy Technology Data Exchange (ETDEWEB)

    Christov, Ivan; Jordan, P M [Code 7181, Naval Research Laboratory, Stennis Space Center, MS 39529-5004 (United States)], E-mail: pjordan@nrlssc.navy.mil

    2008-04-15

    A hyperbolic generalization of Burgers' equation, which includes relaxation, is examined using analytical and numerical tools. By means of singular surface theory, the evolution of initial discontinuities (i.e. shocks) is fully classified. In addition, the parameter space is explored and the bifurcation experienced by the shock amplitude is identified. Then, by means of numerical simulations based on a Godunov-type scheme, we confirm the theoretical findings and explore the solution structure of a signaling-type initial-boundary-value problem with discontinuous boundary data. In particular, we show that diffusive solitons (or Taylor shocks) can emerge in the solution, behind the wavefront. We also show that, for certain parameter values, a shock wave becomes an acceleration wave in infinite time, an unexpected result that is the exact opposite of the well-known phenomenon of finite-time acceleration wave blow-up. Finally, the 'red light turning green' problem is re-examined.

  13. Interaction of solitons with a string of coupled quantum dots

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, Vijendra, E-mail: vsmedphysics@gmail.com; Swami, O. P., E-mail: omg1789@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com [Department of Physics, Govt. Dungar College, Bikaner, Rajasthan 334001 (India); Taneja, S., E-mail: sachintaneja9@gmail.com [Department of Radiotherapy, CHAF Bangalore, Karnataka 560007 (India)

    2016-05-06

    In this paper, we develop a theory for discrete solitons interaction with a string of coupled quantum dots in view of the local field effects. Discrete nonlinear Schrodinger (DNLS) equations are used to describe the dynamics of the string. Numerical calculations are carried out and results are analyzed with the help of matlab software. With the help of numerical solutions we demonstrate that in the quantum dots string, Rabi oscillations (RO) are self trapped into stable bright Rabi solitons. The Rabi oscillations in different types of nanostructures have potential applications to the elements of quantum logic and quantum memory.

  14. Solitons, Bose-Einstein condensation and superfluidity in He II

    International Nuclear Information System (INIS)

    Chela-Flores, J.; Ghassib, H.B.

    1985-09-01

    The analytic form of a wave propagating with a constant velocity and a permanent profile is inferred for a weakly interacting Bose gas, using an exact (rather than asymptotic) solution of the field equation of the self-consistent Hartree model. The significance of this approach is indicated, especially when realistic interatomic potentials are used. In addition, the general relation between solitons and Bose-Einstein condensation is underlined by invoking the profound insight recently acquired in studies of the quantum liquids involved in the living state. It is concluded that solitons may occur in He II, and may play a significant role in the phenomena of superfluidity. (author)

  15. Solitons in ideal optical fibers: a numerical development

    Directory of Open Access Journals (Sweden)

    Eliandro Rodrigues Cirilo

    2010-03-01

    Full Text Available This work developed a numerical procedure for a system of partial differential equations (PDEs describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.

  16. Soliton formation at critical density in laser-irradiated plasmas

    International Nuclear Information System (INIS)

    Anderson, D.; Bondeson, A.; Lisak, M.

    1979-01-01

    The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrodinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrodinger equation are re-examined and found to be more restrictive than previously stated. (author)

  17. Quantized Solitons in the Extended Skyrme-Faddeev Model

    Directory of Open Access Journals (Sweden)

    L. A. Ferreira

    2011-01-01

    Full Text Available The construction of axially symmetric soliton solutions with non-zero Hopf topological charges according to a theory known as the extended Skyrme-Faddeev model, was performed in [1]. In this paper we show how masses of glueballs are predicted within this model.

  18. Solitons, compactons and undular bores in Benjamin–Bona ...

    Indian Academy of Sciences (India)

    2017-01-04

    Jan 4, 2017 ... 3Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India. ∗. Corresponding ... found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term is linear or nonlinear. ... variety of ingenuous mathematical techniques includ-.

  19. Dynamics of coupled field solitons: A collective coordinate approach

    Indian Academy of Sciences (India)

    In this paper we consider a class of systems of two coupled real scalar fields in bidimensional space-time, with the main motivation of studying classical stability of soliton solutions using collective coordinate approach. First, we present the class of systems of the collective coordinate equations which are derived using the ...

  20. Solitons, compactons and undular bores in Benjamin–Bona ...

    Indian Academy of Sciences (India)

    Benjamin–Bona–Mahony-like equations; travelling wave solutions; solitons; compactons; dissipation; undular bores; shock waves. ... 731 235, India; Department of Physics, Abhedananda College, Sainthia 731 234, India; Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata 700 064, India ...

  1. Solitons, compactons and undular bores in Benjamin–Bona ...

    Indian Academy of Sciences (India)

    We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin–Bona–Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton/anticompacton solutions depending on whether the dispersive term islinear ...

  2. Gap solitons in periodic Schrodinger lattice system with nonlinear hopping

    Directory of Open Access Journals (Sweden)

    Ming Cheng

    2016-10-01

    Full Text Available This article concerns the periodic discrete Schrodinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\\alpha\\to 0$. Notice that the nonlinear hopping can be sign changing.

  3. The Big Bang Singularity

    Science.gov (United States)

    Ling, Eric

    The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

  4. Surface Plasmon Singularities

    Directory of Open Access Journals (Sweden)

    Gabriel Martínez-Niconoff

    2012-01-01

    Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.

  5. Breathing pulses in the damped-soliton model for nerves

    Science.gov (United States)

    Fongang Achu, G.; Moukam Kakmeni, F. M.; Dikande, A. M.

    2018-01-01

    Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.

  6. Collective states of externally driven, damped nonlinear Schroedinger solitons

    International Nuclear Information System (INIS)

    Barashenkov, I.V.; Smirnov, Yu.S.

    1997-01-01

    We study bifurcations of localized stationary solitons of the externally driven, damped nonlinear Schroedinger equation iΨ t + Ψ xx + 2|Ψ| 2 Ψ=-iγΨ-h e iΩt , in the region of large γ (γ>1/2). For each pair of h and γ, there are two coexisting solitons, Ψ + and Ψ - . As the driver's strength h increases for the fixed γ, the Ψ + soliton merges with the flat background while the Ψ - forms a stationary collective state with two 'psi-pluses': Ψ - → Ψ (+ - +) . We obtain other stationary solutions and identify them as multisoliton complexes Ψ (++) , Ψ (--) , Ψ (-+) , Ψ (---) , Ψ (-+- ) etc. The corresponding intersoliton separations are compared to predictions of a variational approximation

  7. Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Khater, Mostafa M. A.

    In this article, we study one of the most popular models in nature and also industrial which is the van der Waals normal form for the fluidized granular matter. Understanding of static and dynamic property for these kinds of the models is very important in many aspects of industrial from pharmaceuticals to civil engineering and also some basic physical phenomena like those studied in geophysics. This model explains the phase separation phenomenon. We apply six different methods for this model to obtained the traveling and solitary wave solutions. We make the comparison between obtained solutions with each of them and also with obtained solutions with different methods.

  8. 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

  9. Algorithms in Singular

    Directory of Open Access Journals (Sweden)

    Hans Schonemann

    1996-12-01

    Full Text Available Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]. This includes wellorderings (Buchberger algorithm ([B1], [B2] and tangent cone orderings (Mora algorithm ([M1], [MPT] as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].

  10. Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

    Science.gov (United States)

    Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.

    2010-09-01

    We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

  11. Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

    International Nuclear Information System (INIS)

    Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.

    2010-01-01

    We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

  12. Multi-soliton fusion phenomenon of Burgers equation and fission, fusion phenomenon of Sharma–Tasso–Olver equation

    Directory of Open Access Journals (Sweden)

    Harun Or-Roshid

    2017-06-01

    Full Text Available A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission, fusion phenomena after interaction of the solitons has been discussed. We have considered the Burgers and Sharma–Tasso–Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the solitons, respectively. We improve different structured multi-soliton solutions with possible conditions for fission and fusion of the Burgers and the Sharma–Tasso–Olver equations arises in plasma physics and in ocean dynamics. The amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible condition for fission and fusion is proposed. Furthermore, three-dimensional plots of the wave solutions are given to visualize the dynamics of the model.

  13. Detection of Moving Targets Using Soliton Resonance Effect

    Science.gov (United States)

    Kulikov, Igor K.; Zak, Michail

    2013-01-01

    The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel "soliton resonance" effect in nonlinear dynamical systems. The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the time-dependent data stream obtained with a sensor in form of the "forcing function," which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural "probe" soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent. Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment. The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.

  14. Solitonic Integrable Perturbations of Parafermionic Theories

    CERN Document Server

    Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L

    1997-01-01

    The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.

  15. Solitons, compactons and undular bores in Benjamin-Bona-Mahony-like systems

    Science.gov (United States)

    Saha, Aparna; Talukdar, B.; Das, Umapada; Chatterjee, Supriya

    2017-02-01

    We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin-Bona-Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton /anticompacton solutions depending on whether the dispersive term is linear or nonlinear. We study the influence of increasing nonlinearity of the medium on the soliton and compacton dynamics. The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. The anticompacton solutions are also transformed to undular bores by the effect of dissipation. But the compactons tend to vanish due to viscous effects. The local oscillatory structures behind the bores and /or shock-like waves in the case of solitons and anticompactons are found to depend sensitively both on the coefficient of viscosity and solution of the unperturbed problem.

  16. Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation

    DEFF Research Database (Denmark)

    Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.

    2001-01-01

    The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...

  17. Analytical tools for solitons and periodic waves corresponding to phonons on Lennard-Jones lattices in helical proteins

    DEFF Research Database (Denmark)

    D'ovidio, Francesco; Bohr, Henrik; Lindgård, Per-Anker

    2005-01-01

    We study the propagation of solitons along the hydrogen bonds of an alpha helix. Modeling the hydrogen and peptide bonds with Lennard-Jones potentials, we show that the solitons can appear spontaneously and have long lifetimes. Remarkably, even if no explicit solution is known for the Lennard-Jon...

  18. Numerical Approaches to Spacetime Singularities

    Directory of Open Access Journals (Sweden)

    Beverly K. Berger

    1998-05-01

    Full Text Available This review updates a previous review article. Numerical explorationof the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.

  19. A survey of embedded solitons

    International Nuclear Information System (INIS)

    Fujioka, J.; Espinosa C, A.; Rodriguez, R.F.

    2006-01-01

    At the end of the nineties a brand-new type of soliton was discovered: the embedded solitons. Initially they were found in optical systems, and afterwards they were also found in hydrodynamic models, liquid crystal theory and discrete systems. These peculiar solitary waves are interesting because they exist under conditions in which, until recently, the propagation ol solitons was thought to be impossible. At first these nonlinear waves were believed to be necessarily isolated and unstable, but later on it was found that they can be stable and may exist in families. This paper explains what these embedded solitons are, in which models they have been found, and what variants exist (stable, unstable, continuous, discrete, etc.) (Author)

  20. Statistics of 2D solitons

    International Nuclear Information System (INIS)

    Brekke, L.; Imbo, T.D.

    1992-01-01

    The authors study the inequivalent quantizations of (1 + 1)-dimensional nonlinear sigma models with space manifold S 1 and target manifold X. If x is multiply connected, these models possess topological solitons. After providing a definition of spin and statistics for these solitons and demonstrating a spin-statistics correlation, we give various examples where the solitons can have exotic statistics. In some of these models, the solitons may obey a generalized version of fractional statistics called ambistatistics. In this paper the relevance of these 2d models to the statistics of vortices in (2 + 1)-dimensional spontaneously broken gauge theories is discussed. The authors close with a discussion concerning the extension of our results to higher dimensions

  1. Vector bright soliton behaviors of the coupled higher-order nonlinear Schrödinger system in the birefringent or two-mode fiber.

    Science.gov (United States)

    Liu, Lei; Tian, Bo; Xie, Xi-Yang; Guan, Yue-Yang

    2017-01-01

    Studied in this paper are the vector bright solitons of the coupled higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of two ultrashort pulses in the birefringent or two-mode fiber. With the help of auxiliary functions, we obtain the bilinear forms and construct the vector bright one- and two-soliton solutions via the Hirota method and symbolic computation. Two types of vector solitons are derived. Single-hump, double-hump, and flat-top solitons are displayed. Elastic and inelastic interactions between the Type-I solitons, between the Type-II solitons, and between the two combined types of the solitons are revealed, respectively. Especially, from the interaction between a Type-I soliton and a Type-II soliton, we see that the Type-II soliton exhibits the oscillation periodically before such an interaction and becomes the double-hump soliton after the interaction, which is different from the previously reported.

  2. 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.)

  3. Exact vacuum solutions of the De Witt equation for the closed and open Friedmann models. Operator ordering and the singularity problem

    International Nuclear Information System (INIS)

    Mel'nikov, V.N.; Pevston, G.D.

    1985-01-01

    The authors investigate the Wyler-De Witt vacuum equation of quantum cosmology to obtain exact solutions in the closed and open models. They demonstrate that the operator ordering of De Witt results in nonsingular general solutions in both cases. In the closed model the nonsingular general solution is located on the Planck scale and can be used as a model of the preinflationary universe

  4. Propagation of dispersion-nonlinearity-managed solitons in an inhomogeneous erbium-doped fiber system

    International Nuclear Information System (INIS)

    Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A

    2009-01-01

    In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed

  5. Shocklike soliton because of an impinge of protons and electrons solar particles with Venus ionosphere

    Science.gov (United States)

    Moslem, W. M.; Rezk, S.; Abdelsalam, U. M.; El-Labany, S. K.

    2018-04-01

    This paper introduces an investigation of shocklike soliton or small amplitude Double Layers (DLs) in a collisionless plasma, consisting of positive and negative ions, nonthermal electrons, as well as solar wind streaming protons and electrons. Gardner equation is derived and its shocklike soliton solution is obtained. The model is employed to recognize a possible nonlinear wave at Venus ionosphere. The results indicate that the number densities and velocities of the streaming particles play crucial role to determine the polarity and characteristic features (amplitude and width) of the shocklike soliton waves. An electron streaming speed modifies a negative shocklike wave profile, while an ion streaming speed modulates a positive shocklike wave characteristic.

  6. A two-dimensional soliton system of vortex and Q-ball

    Science.gov (United States)

    Loginov, A. Yu.

    2018-02-01

    The (2 + 1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and a Q-ball. This two-dimensional system is electrically neutral, nevertheless it possesses a nonzero electric field. Moreover, the soliton system has a quantized magnetic flux and a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of topological and nontopological solitons.

  7. Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation

    International Nuclear Information System (INIS)

    Wang Song; Tang Xiaoyan; Lou Senyue

    2004-01-01

    Fission and fusion phenomena can happen for solitons (sometimes solitary waves may be more accurate) which have been recently discovered both theoretically and experimentally. In this paper, taking the Burgers equation and the Sharma-Tasso-Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the soliton solutions respectively which are studied by means of the Hirota's direct method and the Baecklund transformation. Furthermore, the amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible general condition for fission and/or fusion is proposed

  8. Reliable finite element methods for self-adjoint singular perturbation ...

    African Journals Online (AJOL)

    It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...

  9. Solitonic natural orbitals

    Science.gov (United States)

    Cioslowski, Jerzy

    2018-04-01

    The dependence of the natural amplitudes of the harmonium atom in its ground state on the confinement strength ω is thoroughly investigated. A combination of rigorous analysis and extensive, highly accurate numerical calculations reveals the presence of only one positive-valued natural amplitude ("the normal sign pattern") for all ω ≥1/2 . More importantly, it is shown that unusual, weakly occupied natural orbitals (NOs) corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement. These solitonic NOs, whose shapes remain almost invariant as their radial positions drift toward infinity upon the critical values of ω being approached from below, exhibit strong radial localization. Their asymptotic properties are extracted from the numerical data and their relevance to calculations on fully Coulombic systems is discussed.

  10. Noise-induced perturbations of dispersion-managed solitons

    International Nuclear Information System (INIS)

    Li, Jinglai; Spiller, Elaine; Biondini, Gino

    2007-01-01

    We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems

  11. Energy-exchange collisions of dark-bright-bright vector solitons.

    Science.gov (United States)

    Radhakrishnan, R; Manikandan, N; Aravinthan, K

    2015-12-01

    We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

  12. 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....

  13. Singularities in FLRW spacetimes

    Science.gov (United States)

    het Lam, Huibert; Prokopec, Tomislav

    2017-12-01

    We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.

  14. Resolving curvature singularities in holomorphic gravity

    NARCIS (Netherlands)

    Mantz, C.L.M.; Prokopec, T.

    2011-01-01

    We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature

  15. Classical resolution of singularities in dilaton cosmologies

    NARCIS (Netherlands)

    Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK

    2005-01-01

    For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to

  16. 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....

  17. Scaling properties of pure-quartic solitons

    DEFF Research Database (Denmark)

    Blanco-Redondo, Andrea; Lo, Chih Wei; Stefani, Alessio

    2017-01-01

    We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands.......We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands....

  18. Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential.

    Science.gov (United States)

    Li, Min; Xu, Tao

    2015-03-01

    Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

  19. Spatiotemporal solitons in quadratic nonlinear media

    Indian Academy of Sciences (India)

    Optical solitons are localized electromagnetic waves that propagate stably in nonlinear me- dia with group-velocity dispersion (GVD) and/or diffraction. Temporal solitons in single- mode optical fibers are the prototypical optical solitons; these were predicted theoretically in 1973 [1] and first observed experimentally in 1980 ...

  20. On the supersymmetric solitons and monopoles

    International Nuclear Information System (INIS)

    Hruby, J.

    1978-01-01

    The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is mass of the soliton without the quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension