Electro-acoustic solitary waves in dusty plasmas
present a rigorous theoretical investigation of electro- acoustic [particularly, dust-ion acoustic (DIA) and dust-acoustic (DA)] solitary waves in dusty plasmas. We employ the reductive perturbation method for small but finite amplitude solitary waves as well as the pseudo-potential approach for arbitrary amplitude ones. We also analyze the effects of non-planar geometry and dust charge fluctuations on both DIA and DA solitary waves, the effect of finite ion-temperature on DIA solitary waves, and the effects of dust-fluid temperature and non-isothermal ion distributions on DA solitary waves. It has been reported that these effects do not only significantly modify the basic features of DIA or DA solitary waves, but also introduce some important new features. The basic features and the underlying physics of DIA and DA solitary waves, which are relevant to space and laboratory dusty plasmas, are briefly discussed. (author)
Quantum ion-acoustic solitary waves in weak relativistic plasma
Biswajit Sahu
2011-06-01
Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized twospecies relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects signiﬁcantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter on the nature of solitary wave solutions is studied in some detail.
Electron acoustic solitary waves with kappa-distributed electrons
Devanandhan, S; Singh, S V; Lakhina, G S, E-mail: satyavir@iigs.iigm.res.in [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai (India)
2011-08-01
Electron acoustic solitary waves are studied in a three-component, unmagnetized plasma composed of hot electrons, fluid cold electrons and ions having finite temperatures. Hot electrons are assumed to have kappa distribution. The Sagdeev pseudo-potential technique is used to study the arbitrary amplitude electron-acoustic solitary waves. It is found that inclusion of cold electron temperature shrinks the existence regime of the solitons, and soliton electric field amplitude decreases with an increase in cold electron temperature. A decrease in spectral index, {kappa}, i.e. an increase in the superthermal component of hot electrons, leads to a decrease in soliton electric field amplitude as well as the soliton velocity range. The soliton solutions do not exist beyond T{sub c}/T{sub h}>0.13 for {kappa}=3.0 and Mach number M=0.9 for the dayside auroral region parameters.
Effect of nonthermal ion distribution and dust temperature on nonlinear dust-acoustic solitary waves
K Annou; R Annou
2012-01-01
Dust-acoustic solitary waves in unmagnetized dusty plasma whose constituents are inertial charged dust grains, Boltzmannian electrons and nonthermal ions have been investigated by taking into account ﬁnite dust temperature. The pseudopotential has been used to study solitary solution. The existence of solitary waves having negative potential is reported.
Experiments on the acoustic solitary wave generated thermoacoustically in a looped tube
Shimizu, Dai; Sugimoto, Nobumasa
2015-10-01
Emergence of an acoustic solitary wave is demonstrated in a gas-filled, looped tube with an array of Helmholtz resonators connected. The solitary wave is generated thermoacoustically and spontaneously by a pair of stacks positioned diametrically on exactly the opposite side of the loop. The temperature gradient is imposed on both stacks in the same sense along the tube. The stacks made of ceramics and of many square pores are sandwiched by hot and cold heat exchangers. The pressure profile measured and the propagation speed show good agreements with the theoretical ones of the acoustic solitary wave obtained by Sugimoto (J. Acoust. Soc. Am., 99, 1971-1976 (1996)).
Duan Wen-Shan
2004-01-01
The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov-Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.
Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma
Bandyopadhyay, P; Sen, A; Kaw, P K
2008-01-01
The excitation and propagation of finite amplitude low frequency solitary waves are investigated in an Argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Kortweg-de Vries equation.
The influence of dust size distribution on the dust ion acoustic solitary waves in a collisional dusty plasma is investigated. It is found that dust size distribution changes the amplitude and width of a solitary wave. A critical wave number is derived for the existence of purely damping mode. A deformed Korteweg-de Vries (dKdV) equation is obtained for the propagation of weakly nonlinear dust ion acoustic solitary waves and the effect of different plasma parameters on the solution of this equation is also presented
Dust-acoustic solitary waves in a dusty plasma with two-temperature nonthermal ions
Zhi-Jian Zhou; Hong-Yan Wang; Kai-Biao Zhang
2012-01-01
By using reductive perturbation method, the nonlinear propagation of dust-acoustic waves in a dusty plasma (containing a negatively charged dust ﬂuid, Boltzmann distributed electrons and two-temperature nonthermal ions) is investigated. The effects of two-temperature nonthermal ions on the basic properties of small but ﬁnite amplitude nonlinear dust-acoustic waves are examined. It is found that two-temperature nonthermal ions affect the basic properties of the dust-acoustic solitary waves. It is also observed that only compressive solitary waves exist in this system.
S. S. Ghosh
2004-01-01
Full Text Available The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.
Ion-acoustic solitary waves in ultra-relativistic degenerate pair-ion plasmas
The arbitrary and the small amplitude ion-acoustic solitary waves (IASWs) have been studied. The former is studied by using the Sagdeev pseudo-potential approach in a plasma consisting of the degenerate ultrarelativistic electrons, positrons, and the non-relativistic classical ions. It is seen that only compressive solitary waves can propagate through such plasmas. The numerical calculations show that the region of existence of the ion-acoustic solitary waves depends upon the positron (ion) number density and the plasma thermal temperature. This study is appropriate for applications in inertial confinement fusion laboratory research as well as the study of astrophysical dense objects such as white dwarf and dense neutron stars.
El-Labany, S. K.; Behery, E. E. [Department of Physics, Faculty of Science, Damietta University, P.O. Box 34517 New Damietta (Egypt); El-Shamy, E. F. [Department of Physics, Faculty of Science, Damietta University, P.O. Box 34517 New Damietta (Egypt); Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004 Abha (Saudi Arabia)
2013-12-15
The propagation and oblique collision of ion-acoustic (IA) solitary waves in a magnetized dusty electronegative plasma consisting of cold mobile positive ions, Boltzmann negative ions, Boltzmann electrons, and stationary positive/negative dust particles are studied. The extended Poincaré-Lighthill-Kuo perturbation method is employed to derive the Korteweg-de Vries equations and the corresponding expressions for the phase shifts after collision between two IA solitary waves. It turns out that the angle of collision, the temperature and density of negative ions, and the dust density of opposite polarity have reasonable effects on the phase shift. Clearly, the numerical results demonstrated that the IA solitary waves are delayed after the oblique collision. The current finding of this work is applicable in many plasma environments having negative ion species, such as D- and F-regions of the Earth's ionosphere and some laboratory plasma experiments.
Effect of polarization force on the propagation of dust acoustic solitary waves
We report the modifications in the propagation characteristics of dust acoustic solitary waves (DASWs) due to the polarization force acting on micron-size dust particles in a non-uniform plasma. In the small amplitude limit, we derive a K-dV-type equation and show that there is an increase in the amplitude and a reduction in the width of a solitary structure as the polarization force is enhanced for a given Mach number. For arbitrary amplitude waves we employ the Sagdeev potential method and find that the range of Mach numbers where solitary structures can exist becomes narrower in the presence of the polarization interaction. In both limits there exists a critical value of grain size beyond which the DASW cannot propagate.
Effect of polarization force on the propagation of dust acoustic solitary waves
Bandyopadhyay, P; Konopka, U; Khrapak, S A; Morfill, G E [Max-Planck Institut fuer Extraterrestrische Physik, D-85741 Garching (Germany); Sen, A, E-mail: pintu@mpe.mpg.d [Institute for Plasma Research, Bhat, Gandhinagar-382428 (India)
2010-07-15
We report the modifications in the propagation characteristics of dust acoustic solitary waves (DASWs) due to the polarization force acting on micron-size dust particles in a non-uniform plasma. In the small amplitude limit, we derive a K-dV-type equation and show that there is an increase in the amplitude and a reduction in the width of a solitary structure as the polarization force is enhanced for a given Mach number. For arbitrary amplitude waves we employ the Sagdeev potential method and find that the range of Mach numbers where solitary structures can exist becomes narrower in the presence of the polarization interaction. In both limits there exists a critical value of grain size beyond which the DASW cannot propagate.
Oblique propagation of ion-acoustic solitary waves in a magnetized electron-positron-ion plasma
Ferdousi, M.; Sultana, S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-03-15
The properties of obliquely propagating ion-acoustic solitary waves in the presence of ambient magnetic field have been investigated theoretically in an electron-positron-ion nonthermal plasma. The plasma nonthermality is introduced via the q-nonextensive distribution of electrons and positrons. The Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations are derived by adopting reductive perturbation method. The solution of K-dV and modified K-dV equation, which describes the solitary wave characteristics in the long wavelength limit, is obtained by steady state approach. It is seen that the electron and positron nonextensivity and external magnetic field (obliqueness) have significant effects on the characteristics of solitary waves. A critical value of nonextensivity is found for which solitary structures transit from positive to negative potential. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas where static external magnetic field is present.
Heavy-ion-acoustic solitary and shock waves in an adiabatic multi-ion plasma
Hossen, M.A.; Rahman, M.M.; Mamun, A.A., E-mail: armanplasma@gmail.com [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh); Hossen, M.R. [Department of Natural Sciences, Daffodil International University, Dhanmondi, Dhaka (Bangladesh)
2015-08-15
The standard reductive perturbation method has been employed to derive the Korteweg-deVries (K-dV) and Burgers (BG) equations to investigate the basic properties of heavy-ion-acoustic (HIA) waves in a plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The HIA solitary and shock structures are found to exist with either positive or negative potential. It is found that the effects of adiabaticity of inertial heavy ions, nonthermality of electrons, and number densities of plasma components significantly modify the basic properties of the HIA solitary and shock waves. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments. (author)
Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma
Han Jiu-Ning; Luo Jun-Hua; Sun Gui-Hua; Liu Zhen-Lai; Li Shou-Yi
2011-01-01
This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations. The extended Poincaré-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma. The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter He (Hp) on the newly formed wave during interaction, and the phase shift of the colliding solitary waves are studied. It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves. The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.
Nonplanar dust acoustic solitary waves in a strongly coupled dusty plasma with superthermal ions
El-Labany, S. K., E-mail: skellabany@hotmail.com; Zedan, N. A., E-mail: nesreenplasma@yahoo.com [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 Egypt (Egypt); El-Taibany, W. F., E-mail: eltaibany@hotmail.com, E-mail: eltaibany@du.edu.eg [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 Egypt (Egypt); Department of Physics, College of Science for Girls in Abha, King Khalid University, P.O. 960 Abha (Saudi Arabia); El-Shamy, E. F., E-mail: emadel-shamy@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 Egypt (Egypt); Department of Physics, College of Science, King Khalid University, P.O. 9004 Abha (Saudi Arabia)
2014-12-15
The nonplanar amplitude modulation of dust acoustic (DA) envelope solitary waves in a strongly coupled dusty plasma (SCDP) has been investigated. By using a reductive perturbation technique, a modified nonlinear Schrödinger equation (NLSE) including the effects of geometry, polarization, and ion superthermality is derived. The modulational instability (MI) of the nonlinear DA wave envelopes is investigated in both planar and nonplanar geometries. There are two stable regions for the DA wave propagation strongly affected by polarization and ion superthermality. Moreover, it is found that the nonlinear DA waves in spherical geometry are the more structurally stable. The larger growth rate of the nonlinear DA MI is observed in the cylindrical geometry. The salient characteristics of the MI in the nonplanar geometries cannot be found in the planar one. The DA wave propagation and the NLSE solutions are investigated both analytically and numerically.
Ion-acoustic solitary waves and spectrally uniform scattering cross section enhancements
J. Ekeberg
2010-06-01
Full Text Available Spectra measured by incoherent scatter radars are formed predominantly by scattering of the incident signal off ion-acoustic and Langmuir waves in the ionosphere. Occasionally, the upshifted and/or downshifted lines produced by the ion-acoustic waves are enhanced well above thermal levels and referred to as naturally enhanced ion-acoustic lines. In this paper, we study another kind of enhancement, which is spectrally uniform over the whole ion-line, i.e. the up- and downshifted shoulder and the spectral valley in between. Based on observations made with the EISCAT Svalbard radar (ESR facility, we investigate the transient and spectrally uniform power enhancements, which can be explained by ion-acoustic solitary waves. We use a theory of nonlinear waves in a magnetized plasma to determine the properties of such waves and evaluate their effects on scattered signals measured by ESR. We suggest a new mechanism that can explain backscattered power enhancements by one order of magnitude above the thermal level and show that it is consistent with observations.
Gill, Tarsem Singh; Bedi, Chanchal; Bains, Amandeep Singh, E-mail: gillsema@yahoo.co.i [Department of Physics, Guru Nanak Dev University, Amritsar-143005 (India)
2010-05-01
Theoretical studies of the nonlinear self-modulation of ion acoustic waves (IAWs) in an electron-positron-ion plasma with superthermal electrons are carried out. By using the standard reductive perturbation method (RPM), the nonlinear Schroedinger equation (NLSE) is derived. The stability analysis, based on a nonlinear Schroedinger-type equation, exhibits a wide instability region, which depends on spectral index ({kappa}), ratio of positron to electron density (p) and electron to positron temperature ratio ({sigma}). It is found that these parameters modify the nature of modulational instability (MI) for IAWs and associated envelope solitary structures. Further, the effect of these parameters on the growth rate of MI is discussed.
The effects of adiabatic dust grain charge fluctuation and inhomogeneity on the nonlinear properties of dust acoustic (DA) solitary waves are studied. The plasma under consideration is a hot magnetized dusty plasma consisting of negatively charged dust particles, Boltzmann ions, and nonextensive electrons. A modified Zakharov-Kusnetsov equation, which admits a solitary wave solution, is derived using the reductive perturbation theory. It is found that the charge fluctuation of the dust grain modifies the nature of DA solitary structures. The numerical results may be useful to understand phenomena in laboratory and astrophysical plasmas
Employing the reductive perturbation technique, Zakharov–Kuznetzov (ZK) equation is derived for dust acoustic (DA) solitary waves in a magnetized plasma which consists the effects of dust anisotropic pressure, arbitrary charged dust particles, Boltzmann distributed ions, and Kappa distributed superthermal electrons. The ZK solitary wave solution is obtained. Using the small-k expansion method, the stability analysis for DA solitary waves is also discussed. The effects of the dust pressure anisotropy and the electron superthermality on the basic characteristics of DA waves as well as on the three-dimensional instability criterion are highlighted. It is found that the DA solitary wave is rarefactive (compressive) for negative (positive) dust. In addition, the growth rate of instability increases rapidly as the superthermal spectral index of electrons increases with either positive or negative dust grains. A brief discussion for possible applications is included
Sultana, S; Hellberg, M A
2012-01-01
The linear and nonlinear properties of large amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modelled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential type analysis reveals the existence of large amplitude electrostatic solitary waves and allows for an investigation of their propagation characteristics and existence domain, in terms of the soliton speed (Mach number). The effects of the key plasma configuration parameters, namely, the superthermality index and the cold electron density, on the soliton characteristics and existence domain, are studied. The role of obliquen...
Tarsem Singh Gill; Harvinder Kaur
2000-11-01
The effects of nonthermal ion distribution and ﬁnite dust temperature are incorporated in the investigation of nonlinear dust acoustic waves in an unmagnetized dusty plasma. Sagdeev pseudopotential method which takes into account the full nonlinearity of plasma equations, is used here to study solitary wave solutions. Possibility of co-existence of refractive and compressive solitons as a function of Mach number, dust temperature and concentration of nonthermal ions, is considered. For the ﬁxed value of nonthermal ions, it is found that the effect of increase in dust temperature is to reduce the range of co-existence of compressive and refractive solitons. Particular concentration of nonthermal ions results in disappearance of refractive solitons while the decrease in dust temperature, at this concentration restores the lost refractive solitons.
Dust acoustic solitary and shock waves in strongly coupled dusty plasmas with nonthermal ions
Hamid Reza Pakzad; Kurosh Javidan
2009-11-01
The Korteweg–de Vries–Burgers (KdV–Burgers) equation and modified Korteweg–de Vries–Burgers equation are derived in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann distributed electrons. It is found that solitary waves and shock waves can be produced in this medium. The effects of important parameters such as ion nonthermal parameter, temperature, density and velocity on the properties of shock waves and solitary waves are discussed.
LIU Shi-Da; FU Zun-Tao; LIU Shi-Kuo; XIN Guo-Jun; LIANG Fu-Ming
2004-01-01
In this paper, it is shown that the homoclinic orbits exist in iterated functional systems, so do the solitary wave structures. Moreover, Harr father wavelet, Mexican Cap wavelet, and other closed form wavelets have this solitary wave structure, too. So wavelet is a certain kind of solitary wave.
O Rahman; A A Mamun
2013-06-01
A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.
Abdelwahed, H. G. [Department of Physics, College of Sciences and Humanitarian Studies, Salman Bin Abdulaziz University, Al-Kharj (Saudi Arabia); Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura (Egypt); El-Shewy, E. K. [Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura (Egypt)
2012-07-15
Nonlinear ion-acoustic solitary waves in a warm collisionless plasma with nonthermal electrons are investigated by a direct analysis of the field equations. The Sagdeev's potential is obtained in terms of ion acoustic speed by simply solving an algebraic equation. It is found that the amplitude and width of the ion-acoustic solitons as well as the parametric regime where the solitons can exist are sensitive to the population of energetic non-thermal electrons. The soliton and double layer solutions are obtained as a small amplitude approximation.
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
Barman, A
2014-01-01
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive io...
EL-Shamy, E. F., E-mail: emadel-shamy@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta 34517, Egypt and Department of Physics, College of Science, King Khalid University, Abha P.O. 9004 (Saudi Arabia)
2014-08-15
The solitary structures of multi–dimensional ion-acoustic solitary waves (IASWs) have been considered in magnetoplasmas consisting of electron-positron-ion with high-energy (superthermal) electrons and positrons are investigated. Using a reductive perturbation method, a nonlinear Zakharov-Kuznetsov equation is derived. The multi-dimensional instability of obliquely propagating (with respect to the external magnetic field) IASWs has been studied by the small-k (long wavelength plane wave) expansion perturbation method. The instability condition and the growth rate of the instability have been derived. It is shown that the instability criterion and their growth rate depend on the parameter measuring the superthermality, the ion gyrofrequency, the unperturbed positrons-to-ions density ratio, the direction cosine, and the ion-to-electron temperature ratio. Clearly, the study of our model under consideration is helpful for explaining the propagation and the instability of IASWs in space observations of magnetoplasmas with superthermal electrons and positrons.
Jaiswal, S; Sen, A
2016-01-01
We investigate the propagation characteristics of two counter propagating dust acoustic solitary waves (DASWs) undergoing a head-on collision, in the presence of strong coupling between micron sized charged dust particles in a complex plasma. A coupled set of nonlinear dynamical equations describing the evolution of the two DASWs using the extended Poincar?e{Lighthill{Kuo perturbation technique is derived. The nature and extent of post collision phase-shifts of these solitary waves are studied over a wide range of dusty plasma parameters in a strongly and a weakly coupled medium. We ?nd a signi?cant change in the nature and amount of phase delay in the strongly coupled regime as compared to a weakly coupled regime. The phase shift is seen to change its sign beyond a threshold value of compressibility of the medium for a given set of dusty plasma parameters.
Sardar, Sankirtan; Bandyopadhyay, Anup; Das, K. P.
2016-07-01
A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.
Modified ion-acoustic solitary waves in plasmas with field-aligned shear flows
Saleem, H. [Department of Space Science, Institute of Space Technology, 1-Islamabad Highway, Islamabad (Pakistan); Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); Ali, S. [Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); National Centre for Physics (NCP) at Quaid-i-Azam University Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Haque, Q. [Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); National Centre for Physics (NCP) at Quaid-i-Azam University Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan)
2015-08-15
The nonlinear dynamics of ion-acoustic waves is investigated in a plasma having field-aligned shear flow. A Korteweg-deVries-type nonlinear equation for a modified ion-acoustic wave is obtained which admits a single pulse soliton solution. The theoretical result has been applied to solar wind plasma at 1 AU for illustration.
Modified ion-acoustic solitary waves in plasmas with field-aligned shear flows
The nonlinear dynamics of ion-acoustic waves is investigated in a plasma having field-aligned shear flow. A Korteweg-deVries-type nonlinear equation for a modified ion-acoustic wave is obtained which admits a single pulse soliton solution. The theoretical result has been applied to solar wind plasma at 1 AU for illustration
Singh, S. V.; Devanandhan, S.; Lakhina, G. S. [Indian Institute of Geomagnetism, Navi Mumbai (India); Bharuthram, R. [University of the Western Cape, Bellville (South Africa)
2013-01-15
Obliquely propagating ion-acoustic soliatry waves are examined in a magnetized plasma composed of kappa distributed electrons and fluid ions with finite temperature. The Sagdeev potential approach is used to study the properties of finite amplitude solitary waves. Using a quasi-neutrality condition, it is possible to reduce the set of equations to a single equation (energy integral equation), which describes the evolution of ion-acoustic solitary waves in magnetized plasmas. The temperature of warm ions affects the speed, amplitude, width, and pulse duration of solitons. Both the critical and the upper Mach numbers are increased by an increase in the ion temperature. The ion-acoustic soliton amplitude increases with the increase in superthermality of electrons. For auroral plasma parameters, the model predicts the soliton speed, amplitude, width, and pulse duration, respectively, to be in the range of (28.7-31.8) km/s, (0.18-20.1) mV/m; (590-167) m, and (20.5-5.25) ms, which are in good agreement with Viking observations.
Uddin, M. J., E-mail: josim.phys2007@gmail.com; Alam, M. S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-02-15
Nonplanar (cylindrical and spherical) positron-acoustic (PA) Gardner solitary waves (SWs) in an unmagnetized plasma system consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated. The modified Gardner equation is derived by using the reductive perturbation technique. The effects of cylindrical and spherical geometries, superthermal parameter of hot positrons and electrons, relative temperature ratios, and relative number density ratios on the PA Gardner SWs are studied by using the numerical simulations. The implications of our results in various space and laboratory plasma environments are briefly discussed.
LIN Mai-Mai; DUAN Wen-Shan
2007-01-01
In this paper,(2+1)-dimensional electron acoustic waves (EAW) in an unmagnetized collisionless plasma have been studied by the linearized method and the reductive perturbation technique,respectively.The dispersion relation and a modified Kadomtsev-Petviashvili (KP) equation have been obtained for the EAW in the plasma considering a cold electron fluid and a vortex-like hot electrons.It is found from some numerical results that the parameter β (the ratio of the free hot electron temperature to the hot trapped electron temperature) effects on the amplitude and the width of the electron acoustic solitary waves (EASW).It can be indicated that the free hot electron temperature and the hot trapped electron temperature have very important effect on the characters of the propagation for the EASW.
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.
2007-12-01
The solitary structures of the ion-acoustic waves have been considered in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having a vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field. The nonlinear dynamics of ion-acoustic waves in such a plasma is governed by the Schamel's modified Korteweg-de Vries-Zakharov-Kuznetsov (S-ZK) equation. This equation admits solitary wave solutions having a profile sech4. When the coefficient of the nonlinear term of this equation vanishes, the vortex-like velocity distribution function of electrons simply becomes the non-thermal velocity distribution function of electrons and the nonlinear behaviour of the same ion-acoustic wave is described by a Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation. This equation admits solitary wave solutions having a profile sech2. A combined S-KdV-ZK equation more efficiently describes the nonlinear behaviour of an ion-acoustic wave when the vortex-like velocity distribution function of electrons approaches the non-thermal velocity distribution function of electrons, i.e. when the contribution of trapped electrons tends to zero. This combined S-KdV-ZK equation admits an alternative solitary wave solution having a profile different from either sech4 or sech2. The condition for the existence of this alternative solitary wave solution has been derived. It is found that this alternative solitary wave solution approaches the solitary wave solution (the sech2 profile) of the KdV-ZK equation when the contribution of trapped electrons tends to zero. The three-dimensional stability of these solitary waves propagating obliquely to the external uniform and static magnetic field has been investigated by the multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth
Ion-acoustic solitary waves and spectrally uniform scattering cross section enhancements
J. Ekeberg; Wannberg, G.; Eliasson, L; Stasiewicz, K.
2010-01-01
Spectra measured by incoherent scatter radars are formed predominantly by scattering of the incident signal off ion-acoustic and Langmuir waves in the ionosphere. Occasionally, the upshifted and/or downshifted lines produced by the ion-acoustic waves are enhanced well above thermal levels and referred to as naturally enhanced ion-acoustic lines. In this paper, we study another kind of enhancement, which is spectrally uniform over the whole ion-line, i.e. the up- and downshifted shoulder and t...
A theoretical investigation is carried out to study the existence and characteristics of propagation of dust-acoustic (DA) waves in an electron-depleted dusty plasma with two-temperature ions, which are modeled by kappa distribution functions. A three-dimensional cylindrical Kadomtsev-Petviashvili equation governing evolution of small but finite amplitude DA waves is derived by means of a reductive perturbation method. The influence of physical parameters on solitary wave structure is examined. Furthermore, the energy integral equation is used to study the existence domains of the localized structures. It is found that the present model can be employed to describe the existence of positive as well as negative polarity DA solitary waves by selecting special values for parameters of the system, e.g., superthermal index of cold and/or hot ions, cold to hot ion density ratio, and hot to cold ion temperature ratio. This model may be useful to understand the excitation of nonlinear DA waves in astrophysical objects.
Exciton solitary waves (exolitons)
The soliton theory is briefly explained with regard to cooperative phenomena in one-dimensional systems. The study of the dynamics of a one-dimensional lattice shows that nonlinear phonon interaction results in the production of a solitary wave. The procedure is indicated for the mathematical solution of the problem of the exciton-phonon interaction. (M.S.)
Solitary waves on nonlinear elastic rods. I
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Solitary waves on tensegrity lattices
Fraternali, F.; Senatore, L.; Daraio, C.
2012-06-01
We study the dynamics of lattices formed by masses connected through tensegrity prisms. By employing analytic and numerical arguments, we show that such structures support two limit dynamic regimes controlled by the prisms' properties: (i) in the low-energy (sonic) regime the system supports the formation and propagation of solitary waves which exhibit sech2 shape and (ii) in the high-energy (ultrasonic) regime the system supports atomic-scale localization. Such peculiar features found in periodic arrays of tensegrity structures suggest their use for the creation of new composite materials (here called "tensegrity materials") of potential interest for applications in impact absorption, energy localization and in new acoustic devices.
CHEN Jian-Hong; WEI Nan-Xia
2009-01-01
Taking into account the combined effects of the external magnetic field, adiabatic dust charge fluctuation and collisions occurring between the charged dust gains and neutral gas particles (dust-neutral collisions), the dust-acoustic solitary waves in three-dimensional uniform dusty plasmas are investigated analytically. By using the reductive perturbation method, the Korteweg-de Vries (KdV) equation governing the dust-acoustic solitary waves is obtained. The present analytical results show that only rarefactive solitary waves exist in this system. It is also found that the effects of the wave vector along the z-direction, dust charge variation, collisional frequency, the plasma density, and temperature ratio can significantly influence the characteristics of low-frequency wave modes. Moreover, for the collisional dusty plasmas, there is a certain critical value μc of the plasma density ratio #, if μ < μc, the width of the waves increases with μ, otherwise the width of waves decreases with μ.
Uday Narayan Ghosh; Prasantha Chatterjee; Deb Kumar Ghosh
2013-10-01
Interaction of nonplanar ion-acoustic solitary waves is an important source of information for studying the nature and characteristics of ion-acoustic solitary waves (IASWs). The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising of nonthermal distributed electrons and warm ions is investigated using the extended version of Poincaré–Lighthill–Kuo (PLK) perturbation method. How the interactions are taking place in cylindrical and spherical geometries are shown numerically. Analytical phase shifts are derived for nonplanar geometry. The effects of the ion to electron temperature parameter and the nonthermal electrons parameter on the phase shift are studied. It is shown that the properties of the interaction of IASWs in different geometries are very different.
Merriche, Abderrzak; Ait Gougam, Leila; Tribeche, Mouloud
2016-01-01
The problem of the head-on collision of two ion-acoustic solitary waves (IASWs) is addressed in electronegative plasmas with a nonextensive electron velocity distribution. Our plasma model is inspired from the experimental studies of Ichiki et al. (2001). Using the extended Poincare-Lighthill-Kuo (PLK) perturbation method, the phase shifts of the head-on collision are obtained. Analytical and numerical results reveal that the magnitude of the phase shift of the IASWs depends sensitively on the number density ratios μ and υ, the mass ratio σ as well as the nonextensive parameter q. For a given mass ratio σ ≃ 0.27 (Ar+ - SF6-), the magnitude of the phase shift increases with an increase of the nonextensive parameter q. An increase of the electron-to-positive ion density ratio μ lowers the phase shift, a trend which is much perceptible for q > 1. As σ increases [ σ ≃ 0.89 (Xe+ - SF6-) ], the phase shift becomes larger.
Global Attraction to Solitary Waves
Komech, Andrey
2009-01-01
The long time asymptotics for nonlinear wave equations have been the subject of intensive research, starting with the pioneering papers by Segal, Strauss, and Morawetz, where the nonlinear scattering and local attraction to zero were considered. Global attraction (for large initial data) to zero may not hold if there are quasistationary solitary wave solutions. We will call such solutions "solitary waves". Other appropriate names are "nonlinear eigenfunctions" and "quantum stationary states"....
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.; Das
2014-02-01
Schamel's modified Korteweg-de Vries-Zakharov-Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech 4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k 2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k 2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k 2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.
Mamun, A A; Ashrafi, K S; Shukla, P K
2010-08-01
A strongly coupled dusty plasma containing strongly correlated negatively charged dust grains and weakly correlated (Maxwellian) electrons and ions has been considered. The effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains) and effective dust temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure) on the dust-acoustic (DA) solitary and shock waves propagating in such a strongly coupled dusty plasma are taken into account. The DA solitary and shock waves are found to exist with negative potential only. It has been shown that the strong correlation among the charged dust grains is a source of dissipation and is responsible for the formation of the DA shock waves. It has also been shown that the effects of polarization force and effective dust-temperature significantly modify the basic features (e.g., amplitude, width, and speed) of the DA solitary and shock waves. It has been suggested that a laboratory experiment be performed to test the theory presented in this work. PMID:20866924
Shahmohammadi, Nafise; Dorranian, Davoud
2015-10-01
Simultaneous effects of dust charge fluctuation and nonthermal ions on the threshold point and growth rate of three-dimensional instability of dust-acoustic solitary waves (DASW) in magnetized dusty plasma have been investigated. In this model, dusty plasma consists of Maxwellian electrons, nonthermal ions, and micron size negatively charged dust particles. Modified Zakharov-Kuznetsov equation for DASW was derived employing a reductive perturbation method and its solitary answer under the influence of dust charge fluctuation and nonthermal ions has been studied. The dispersion relation of DASW has been derived using a small-k perturbation method. Results show that the direction and the magnitude of external magnetic field at which the instability takes place are strongly affected by the rate of dust charge fluctuation and nonthermality of ions. With increasing the number of nonthermal ions, the growth rate of instability decreases, while increasing the dust charge fluctuation increases the growth rate of instability.
Shahmohammadi, Nafise; Dorranian, Davoud, E-mail: doran@srbiau.ac.ir [Laser Lab., Plasma Physics Research Center, Science and Research Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)
2015-10-15
Simultaneous effects of dust charge fluctuation and nonthermal ions on the threshold point and growth rate of three-dimensional instability of dust-acoustic solitary waves (DASW) in magnetized dusty plasma have been investigated. In this model, dusty plasma consists of Maxwellian electrons, nonthermal ions, and micron size negatively charged dust particles. Modified Zakharov-Kuznetsov equation for DASW was derived employing a reductive perturbation method and its solitary answer under the influence of dust charge fluctuation and nonthermal ions has been studied. The dispersion relation of DASW has been derived using a small-k perturbation method. Results show that the direction and the magnitude of external magnetic field at which the instability takes place are strongly affected by the rate of dust charge fluctuation and nonthermality of ions. With increasing the number of nonthermal ions, the growth rate of instability decreases, while increasing the dust charge fluctuation increases the growth rate of instability.
Simultaneous effects of dust charge fluctuation and nonthermal ions on the threshold point and growth rate of three-dimensional instability of dust-acoustic solitary waves (DASW) in magnetized dusty plasma have been investigated. In this model, dusty plasma consists of Maxwellian electrons, nonthermal ions, and micron size negatively charged dust particles. Modified Zakharov-Kuznetsov equation for DASW was derived employing a reductive perturbation method and its solitary answer under the influence of dust charge fluctuation and nonthermal ions has been studied. The dispersion relation of DASW has been derived using a small-k perturbation method. Results show that the direction and the magnitude of external magnetic field at which the instability takes place are strongly affected by the rate of dust charge fluctuation and nonthermality of ions. With increasing the number of nonthermal ions, the growth rate of instability decreases, while increasing the dust charge fluctuation increases the growth rate of instability
Shallow Water Waves and Solitary Waves
Hereman, Willy
2013-01-01
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow Water Wave Equations of Geophysical Fluid Dynamics; Computation of Solitary Wave Solutions; Numerical Methods; Water Wave Experiments and Observations; Future Directions, and Bibliography.
Solitary waves and homoclinic orbits
The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids. More specifically, it centres around the mathematical description of solitary waves in a single spatial dimension. Moreover, it concentrates on strongly dissipative dynamics, rather than integrable systems like the KdV equation. One-dimensional solitary waves, or pulses and fronts as they are also called, are the simplest kinds of coherent structure (at least from a geometrical point of view). Nevertheless, their dynamics can be rich and complicated. In some circumstances this leads to the formation of spatio-temporal chaos in the systems giving birth to the solitary waves, and understanding that phenomenon is one of the major goals in the theory outlined in this review. Unfortunately, such a goal is far from achieved to date, and the author assess its current status and incompleteness
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.
The Korteweg de Varies Zakharov Kuznetsov (KdV ZK) equation describes the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external magnetic field in a non-thermal plasma consisting of warm adiabatic ions. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion-acoustic wave is described by a modified KdV ZK (MKdV ZK) equation. A combined MKdV KdV ZK equation more efficiently describes the nonlinear behaviour of ion-acoustic waves at points in the neighbourhood of the curve in the parametric plane along which the coefficient of the nonlinear term of the KdV ZK equation vanishes. This combined MKdV KdV ZK equation admits both double-layer and alternative solitary-wave solutions having profile different from sech(2) or sech. In this paper the three-dimensional stability of the alternative solitary-wave solution having profile different from sech(2) or sech has been investigated by the recently developed multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of instability have been derived at the lowest order. The correct expression of the growth rate of instability at the lowest order has been obtained for a limiting case and the stability analysis has been carried out numerically from our model as presented in this paper for arbitrary values of the parameters involved in the system.
Oblique solitary waves in a five component plasma
Sijo, S.; Manesh, M.; Sreekala, G.; Venugopal, C., E-mail: cvgmgphys@yahoo.co.in [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, 686 560 Kerala (India); Neethu, T. W. [Department of Physics, CMS College, Mahatma Gandhi University, Kottayam, 686 001 Kerala (India); Renuka, G. [Kerala State Council for Science, Technology and Environment, Thiruvananthapuram, 695 004 Kerala (India)
2015-12-15
We investigate the influence of a second electron component on oblique dust ion acoustic solitary waves in a five component plasma consisting of positively and negatively charged dust, hydrogen ions, and hotter and colder electrons. Of these, the heavier dust and colder photo-electrons are of cometary origin while the other two are of solar origin; electron components are described by kappa distributions. The K-dV equation is derived, and different attributes of the soliton such as amplitude and width are plotted for parameters relevant to comet Halley. We find that the second electron component has a profound influence on the solitary wave, decreasing both its amplitude and width. The normalized hydrogen density strongly influences the solitary wave by decreasing its width; the amplitude of the solitary wave, however, increases with increasing solar electron temperatures.
The effect of dust size, mass and charge distributions on the characteristics of nonlinear dust acoustic solitary waves (DASW) in a two-temperature ion dusty plasma has been studied analytically. The mass and electrical charge of dust particles are assumed to be proportional with their size. Plasma is embedded in an external magnetic field with variable direction. Using a reductive perturbation method, the Zakharov–Kuznetsov (ZK) equation is derived and its solitary answers are extracted. The coefficients of the nonlinear term of the ZK equation are affected strongly by the size of dust particles when the relative size (the ratio of the largest dust radius to smallest dust radius) is less than 2. Both the width and amplitude of DASW increase with increasing relative size. The cyclotron frequency of the dust changes with the relative size of the dust particles. DASW width is influenced by the magnitude as well as direction of the external magnetic field, while its amplitude is independent of the magnitude of the external magnetic field. At each strength of the external magnetic field, there is an optimum magnitude for its direction at which the width of DASW is maximum
J. Z. G. Ma
2010-05-01
Full Text Available Lower-hybrid (LH oscillitons reveal one aspect of geocomplexities. They have been observed by rockets and satellites in various regions in geospace. They are extraordinary solitary waves the envelop of which has a relatively longer period, while the amplitude is modulated violently by embedded oscillations of much shorter periods. We employ a two-fluid (electron-ion slab model in a Cartesian geometry to expose the excitation of LH oscillitons. Relying on a set of self-similar equations, we first produce, as a reference, the well-known three shapes (sinusoidal, sawtooth, and spiky or bipolar of parallel-propagating ion-acoustic (IA solitary structures in the absence of electron inertia, along with their Fast Fourier Transform (FFT power spectra. The study is then expanded to illustrate distorted structures of the IA modes by taking into account all the three components of variables. In this case, the ion-cyclotron (IC mode comes into play. Furthermore, the electron inertia is incorporated in the equations. It is found that the inertia modulates the coupled IA/IC envelops to produce LH oscillitons. The newly excited structures are characterized by a normal low-frequency IC solitary envelop embedded by high-frequency, small-amplitude LH oscillations which are superimposed upon by higher-frequency but smaller-amplitude IA ingredients. The oscillitons are shown to be sensitive to several input parameters (e.g., the Mach number, the electron-ion mass/temperature ratios, and the electron thermal speed. Interestingly, whenever a LH oscilliton is triggered, there occurs a density cavity the depth of which can reach up to 20% of the background density, along with density humps on both sides of the cavity. Unexpectedly, a mode at much lower frequencies is also found beyond the IC band. Future studies are finally highlighted. The appendices give a general dispersion relation and specific ones of linear modes relevant to all the nonlinear modes encountered
Bulk solitary waves in elastic solids
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
Multi-component optical solitary waves
Kivshar, Y. S.; Sukhorukov, A. A.; Ostrovskaya, E. A.;
2000-01-01
We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for highperformance computer networks......, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices. (C) 2000 Elsevier Science B.V. All rights reserved....
Oblique propagation of dust ion-acoustic solitary waves in a magnetized dusty pair-ion plasma
Misra, A P
2013-01-01
We study the linear and nonlinear properties of electrostatic waves in a magnetized pair-ion plasma with immobile positively charged dusts. For the obliquely propagating linear waves, a general dispersion relation is derived, from which it is shown that the low-frequency (in comparison with the negative-ion cyclotron frequency) long-wavelength "slow" and a "fast" modes can propagate as dust ion-acoustic (DIA) and dust ion-cyclotron (DIC)-like waves. The properties of these modes are analyzed with the effects of obliqueness of propagation $(\\theta)$, the negative to positive ion mass ratio $(m)$, the ratio of negative to positive ion temperatures $(T)$, the static magnetic field as well as the presence of charged dusts (characterized by the dust to negative-ion number density $\\delta$) in the plasma. In the nonlinear regime, a standard reductive perturbation technique is used to derive a Korteweg-de Vries (KdV) equation for the oblique DIA waves. We show that the KdV equation can admit either compressive or ra...
Instability of large solitary water waves
Lin, Zhiwu
2008-01-01
We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120 degree angle at the crest. Under the assumption of non-existence of secondary bifurcation which is confirmed numerically, we prove linear instability of solitary waves which are higher than the wave of maximal energy and lower than the wave of maximal travel speed. It is also shown that there exist uns...
Transversally periodic solitary gravity-capillary waves.
Milewski, Paul A; Wang, Zhan
2014-01-01
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity-capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922
In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement
Demiray, Hilmi, E-mail: demiray@isikun.edu.tr [Department of Mathematics, Faculty of Arts and Sciences, Işık University, 34980 Şile-İstanbul (Turkey); Bayındır, Cihan, E-mail: cihan.bayindir@isikun.edu.tr [Department of Civil Engineering, Faculty of Engineering, Işık University, 34980 Şile-İstanbul (Turkey)
2015-09-15
In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.
2007-09-01
The purpose of this paper is to present the recent work of Das et al. [J. Plasma Phys. 72, 587 (2006)] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a more generalized form. Here we derive the alternative solitary wave solution of variable width instead of fixed width of the combined MKdV-KdV-ZK equation along with the condition for its existence and find that this solution assumes the sech profile of the MKdV-ZK (Modified Korteweg-de Vries-Zakharov-Kuznetsov) equation, when the coefficient of the nonlinear term of the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation tends to zero. The three-dimensional stability analysis of the alternative solitary wave solution of variable width of the combined MKdV-KdV-ZK equation shows that the instability condition and the first order growth rate of instability are exactly the same as those of the solitary wave solution (the sech profile) of the MKdV-ZK equation, when the coefficient of the nonlinear term of the KdV-ZK equation tends to zero.
Alam, M. S.; Uddin, M. J.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh); Masud, M. M. [Department of Physics, Bangladesh University of Engineering and Technology, Dhaka (Bangladesh)
2014-09-01
Positron-acoustic (PA) solitary waves (SWs) and double layers (DLs) in four-component plasmas consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated both numerically and analytically by deriving Korteweg–de Vries (K-dV), modified K-dV (mK-dV), and Gardner equations along with their DLs solutions using the reductive perturbation method. It is examined that depending on the plasma parameters, the K-dV SWs, Gardner SWs, and DLs support either compressive or rarefactive structures, whereas mK-dV SWs support only compressive structure. It is also found that the presence of superthermal (kappa distributed) hot positrons and hot electrons significantly modify the basic features of PA SWs as well as PA DLs. Besides, the critical number density ratio of hot positrons and cold positrons play an important role in the polarity of PA SWs and DLs. The implications of our results in different space as well as laboratory plasma environments are briefly discussed.
Conservative numerical methods for solitary wave interactions
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
Exact solitary wave solutions of nonlinear wave equations
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Asymptotic Stability of Ascending Solitary Magma Waves
Simpson, Gideon; Weinstein, Michael I.
2008-01-01
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to evolving material parameters to model partially molten rock, magma, in the Earth's interior. Solitary waves are also found here, but the equations lack useful mathematical structures such as an inverse scattering transform or even a variational formulation. A c...
Navier Stokes model of solitary wave collision
Wave collision and its interaction characteristics is one of the important challenges in coastal engineering. This article concerns the collision of solitary waves over a horizontal bottom considering unsteady, incompressible viscous flow with free surface. The method solves the two dimensional Naiver–Stokes equations for conservation of momentum, continuity equation, and full nonlinear kinematic free-surface equation for Newtonian fluids, as the governing equations in a vertical plan. A mapping was developed to trace the deformed free surface encountered during wave propagation, transforms and interaction by transferring the governing equations from the physical domain to a computational domain. Also a numerical scheme is developed using finite element modeling technique in order to predict the solitary wave collision. Consequently results compared with other researches and show the inelastic behavior of solitary wave collision
Dust ion acoustic solitary structures in presence of nonthermal electrons and isothermal positrons
Paul, Ashesh; Bandyopadhyay, Anup
2016-05-01
Arbitrary amplitude dust ion acoustic solitary structures have been investigated in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons and isothermal positrons. A computational scheme has been developed to draw the qualitatively different existence domains or compositional parameter spaces showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers, coexistence of solitary waves of both polarities and positive potential supersolitons.
Solitary Wave Propagation Influenced by Submerged Breakwater
王锦; 左其华; 王登婷
2013-01-01
The form of Boussinesq equation derived by Nwogu (1993) using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method (WCCM) was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.
Solitary Wave Interactions in Granular Media
WEN Zhen-Ying; WANG Shun-Jin; ZHANG Xiu-Ming; LI Lei
2007-01-01
We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝δn, with 5/2 ≤n≤3 and δ≥0,δbeing the bead-bead overlap. There are two collision types of solitary waves, overtaking collision and head-on collision, in the chain of beads. Our quantitative results show that after collision the large solitary wave gains energy and the small one loses energy for overtaking type while the large one loses energy, and the small one gains energy for head-on type. The scattering effects decrease with n for overtaking collision whereas increase with n for head-on collision.
Interaction dynamics of electrostatic solitary waves
V. L. Krasovsky
1999-01-01
Full Text Available Interaction of nonlinear electrostatic pulses associated with electron phase density holes moving in a collisionless plasma is studied. An elementary event of the interaction is analyzed on the basis of the energy balance in the system consisting of two electrostatic solitary waves. It is established that an intrinsic property of the system is a specific irreversibility caused by a nonadiabatic modification of the internal structure of the holes and their effective heating in the process of the interaction. This dynamical irreversibility is closely connected with phase mixing of the trapped electrons comprising the holes and oscillating in the varying self-consistent potential wells. As a consequence of the irreversibility, the "collisions" of the solitary waves should be treated as "inelastic" ones. This explains the general tendency to the merging of the phase density holes frequently observed in numerical simulation and to corresponding coupling of the solitary waves.
Asymptotic linear stability of solitary water waves
Pego, Robert L
2010-01-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (i.e., symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Asymptotic linear stability of solitary water waves
Pego, Robert L.; Sun, Shu-Ming
2010-01-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay a...
Scattering of solitary waves in granular media
Vergara, Lautaro
2005-01-01
A detailed numerical study of the scattering of solitary waves by a barrier, in a granular media with Hertzian contact, shows the existence of secondary multipulse structures generated at the interface of two "sonic vacua", which have a similar structure as the one previously found by Nesterenko and coworkers.
Solitary Wave Solutions for Zoomeron Equation
Amna IRSHAD
2013-04-01
Full Text Available Tanh-Coth Method is applied to find solitary wave solutions of the Zoomeron equation which is of extreme importance in mathematical physics. The proposed scheme is fully compatible with the complexity of the problem and is highly efficient. Moreover, suggested combination is capable to handle nonlinear problems of versatile physical nature.
Solitary waves on nonlinear elastic rods. II
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.;
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
Study on Solitary Waves of a General Boussinesq Model
无
2007-01-01
In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.
Asymmetric gravity-capillary solitary waves on deep water
Z. Wang; Vanden-Broeck, J-M; Milewski, P. A.
2014-01-01
We present new families of gravity–capillary solitary waves propagating on the surface of a two-dimensional deep fluid. These spatially localised travelling-wave solutions are non-symmetric in the wave propagation direction. Our computation reveals that these waves appear from a spontaneous symmetry-breaking bifurcation, and connect two branches of multi-packet symmetric solitary waves. The speed–energy bifurcation curve of asymmetric solitary waves features a zigzag behaviour with one or mor...
Solitary kinetic Alfven waves in adiabatic process
Solitary kinetic Alfven waves (SKAWs) have been an important subject in the field of space plasma physics because of their nonzero parallel electrical field and density fluctuations. Under different thermodynamic processes, SKAWs, within the limit of small amplitude, are studied analytically and numerically using the Sagdeev potential method. The results show that the width of the solitary structures is larger and the amplitude of the density humps is smaller under constant entropy than those under constant temperature with other relevant parameters being the same. The perturbed electromagnetic fields Ex, By, and Ez are also studied further.
Ghosh, S. S., E-mail: sukti@iigs.iigm.res.in [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410218 (India); Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, Kolkata 700064 (India)
2014-08-15
It is observed that the presence of a minority component of cooler electrons in a three component plasma plays a deterministic role in the evolution of solitary waves, double layers, or the newly discovered structures called supersolitons. The inclusion of the cooler component of electrons in a single electron plasma produces sharp increase in nonlinearity in spite of a decrease in the overall energy of the system. The effect maximizes at certain critical value of the number density of the cooler component (typically 15%–20%) giving rise to a hump in the amplitude variation profile. For larger amplitudes, the hump leads to a forbidden region in the ambient cooler electron concentration which dissociates the overall existence domain of solitary wave solutions in two distinct parameter regime. It is observed that an inclusion of the cooler component of electrons as low as < 1% affects the plasma system significantly resulting in compressive double layers. The solution is further affected by the cold to hot electron temperature ratio. In an adequately hotter bulk plasma (i.e., moderately low cold to hot electron temperature ratio), the parameter domain of compressive double layers is bounded by a sharp discontinuity in the corresponding amplitude variation profile which may lead to supersolitons.
Bright Solitary Waves in Malignant Gliomas
Pérez-García, Víctor M.; Calvo, Gabriel F.; Belmonte-Beitia, Juan; Diego, D.; Pérez-Romasanta, Luis
2011-01-01
We put forward a nonlinear wave model describing the fundamental physio-pathologic features of an aggressive type of brain tumors: glioblastomas. Our model accounts for the invasion of normal tissue by a proliferating and propagating rim of active glioma cancer cells in the tumor boundary and the subsequent formation of a necrotic core. By resorting to numerical simulations, phase space analysis and exact solutions, we prove that bright solitary tumor waves develop in such systems.
Weierstrass's criterion and compact solitary waves
Destrade, Michel; Saccomandi, Giuseppe
2007-01-01
Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to identify some differential equations for which compact and even semicompact traveling solitary waves exist. In the framework of continuum mechanics, these differential equations correspond to bulk shear waves for a special class of constitutive laws.
Instability of nonlinear dispersive solitary waves
Lin, Zhiwu
2008-01-01
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain criteria for the existence of exponentially growing solutions to the linearized problem. The novelty is that we dealt with models with nonlocal dispersive terms, for which the spectra problem is out of reach by the Evans function technique. For the proof, ...
Frustrated Brownian Motion of Nonlocal Solitary Waves
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
The lifecycle of axisymmetric internal solitary waves
J. M. McMillan
2010-09-01
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r^{-p} with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r^{-1}.
Dynamics of Gravity-Capillary Solitary Waves in Deep Water
Wang, Zhan
2012-01-01
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential flow problem by taking a cubic truncation of the scaled Dirichlet-to-Neumann operator for the normal velocity on the free surface. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain. Fully localised solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. The solitary wave branches are indexed by their finite energy at small amplitude, and the dynamics of the solitary waves is complex involving nonlinear focussing of wave packets, quasi-elastic collisions, and the generation of propagating, spatially lo...
Paul, Ashesh
2016-01-01
Employing the Sagdeev pseudo-potential technique the ion acoustic solitary structures have been investigated in an unmagnetized collisionless plasma consisting of adiabatic warm ions, nonthermal electrons and isothermal positrons. The qualitatively different compositional parameter spaces clearly indicate the existence domains of solitons and double layers with respect to any parameter of the present plasma system. The present system supports the negative potential double layer which always restricts the occurrence of negative potential solitons. The system also supports positive potential double layers when the ratio of the average thermal velocity of positrons to that of electrons is less than a critical value. However, there exists a parameter regime for which the positive potential double layer is unable to restrict the occurrence of positive potential solitary waves and in this region of the parameter space, there exist positive potential solitary waves after the formation of a positive potential double ...
Solitary Wave and Wave Front as Viewed From Curvature
LIUShi-Kuo; FUZun-Tao; LIUShi-Da; LIANGFu-Ming; XINGuo-Jun
2004-01-01
The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s),which varies with arc length s. For solitary wave when s→±∞, then its curvature c(s) approaches zero, and whens = 0, the curvature c(s) reaches its maximum. For wave front, when s→±∞, then its curvature c(s) approaches zero,and when s = 0, the curvature c(s) is still zero, but c'(s)≠0. That is, s = 0 is a turning point. When c(s) is given,the variance at some point (x, y) in stream line with arc length s satisfies a 2-order linear variable-coeffcient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.
Electron-acoustic_solitary_structures_in_two-electron-temperature_plasma_with_superthermal_electrons
Chen, H
2011-01-01
The propagation of nonlinear electron- acoustic waves (EAWs) in an unmagnetized collision- less plasma system consisting of a cold electron fluid, superthermal hot electrons and stationary ions is investigated. A reductive perturbation method is employed to obtain a modified Korteweg-de Vries (mKdV) equa- tion for the first-order potential. The small amplitude electron-acoustic solitary wave, e.g., soliton and dou- ble layer (DL) solutions are presented, and the effects of superthermal electrons on the nature of the solitons are also discussed. But the results shows that the weak stationary EA DLs cannot be supported by the present model.
Solitary waves and their linear stability in nonlinear lattices
Hwang, Guenbo; Yang, Jianke
2011-01-01
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, hinge upon a certain recurrence relation which contains information beyond all orders of the usual two-scale perturbation expansion. It follows that only two such positions are permissible, and of those two solitary waves, one is linearly stable and the other unstable. For a cosine lattice, in particular, the two possible solitary waves are centered at a maximum or minimum of the lattice, with the former being stable, and the analytical predictions for the associated linear stability eigenvalues are in excellent agreement with numerical results. Furthermore, a countable set of multi-solitary-wave bound states are const...
Stable complex solitary waves of Sasa Satsuma equation
Sasanka Ghosh
2001-11-01
Existence of a new class of complex solitary waves is shown for Sasa Satsuma equation. These solitary waves are found to be stable in a certain domain of the parameter and become chaotic if the parameter exceeds the value 2.4. Signiﬁcantly, the complex solitary waves propagate at higher bit rate over the most stable solitons under the same conditions of the input parameters.
A plethora of generalised solitary gravity-capillary water waves
Clamond, Didier; Dutykh, Denys; Durán, Angel
2015-01-01
The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of (likely) an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domai...
Interactions of large amplitude solitary waves in viscous fluid conduits
Lowman, Nicholas K; El, Gennady A
2013-01-01
The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves. We use numerical simulations and experimental observations to extend the classification scheme to the strongly nonlinear regime for viscous conduit solitary waves, where we identify three classes of nonlinear interaction behavior: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves are approximately solitons. Experimental data are shown to be in excellent agreemen...
Mehdipoor, M.; Neirameh, A.
2012-01-01
The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries (K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions of the K-dV equation investigated, through the ( G'/ G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary waves in Thomas-Fermi plasmas.
Solitary waves in asymmetric electron-positron-ion plasmas
Lu, Ding; Li, Zi-Liang; Xie, Bai-Song
2015-10-01
> By solving the coupled equations of the electromagnetic field and electrostatic potential, we investigate solitary waves in an asymmetric electron-positron plasma and/or electron-positron-ion plasmas with delicate features. It is found that the solutions of the coupled equations can capture multipeak structures of solitary waves in the case of cold plasma, which are left out by using the long-wavelength approximation. By considering the effect of ion motion with respect to non-relativistic and ultra-relativistic temperature plasmas, we find that the ions' mobility can lead to larger-amplitude solitary waves; especially, this becomes more obvious for a high-temperature plasma. The effects of asymmetric temperature between electrons and positrons and the ion fraction on the solitary waves are also studied and presented. It is shown that the amplitudes of solitary waves decrease with positron temperature in asymmetric temperature electron-positron plasmas and decrease also with ion concentration.
Impact induced solitary wave propagation through a woodpile structure
Kore, R.; Waychal, A.; Agarwal, S.; Yadav, P.; Uddin, Ahsan; Sahoo, N.; Shelke, A.
2016-02-01
In this paper, we investigate solitary wave propagation through a one-dimensional woodpile structure excited by low and high velocity impact. Woodpile structures are a sub-class of granular metamaterial, which supports propagation of nonlinear waves. Hertz contact law governs the behavior of the solitary wave propagation through the granular media. Towards an experimental study, a woodpile structure was fabricated by orthogonally stacking cylindrical rods. A shock tube facility has been developed to launch an impactor on the woodpile structure at a velocity of 30 m s-1. Embedded granular chain sensors were fabricated to study the behavior of the solitary wave. The impact induced stress wave is studied to investigate solitary wave parameters, i.e. contact force, contact time, and solitary wave velocity. With the aid of the experimental setup, numerical simulations, and a theoretical solution based on the long wavelength approximation, formation of the solitary wave in the woodpile structure is validated to a reasonable degree of accuracy. The nondispersive and compact supported solitary waves traveling at sonic wave velocity offer unique properties that could be leveraged for application in nondestructive testing and structural health monitoring.
Analytical study of dissipative solitary waves
Dini, Fatemeh [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Emamzadeh, Mehdi Molaie [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Khorasani, Sina [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Bobin, Jean Louis [Universite Pierre et Marie Curie, Paris (France); Amrollahi, Reza [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Sodagar, Majid [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Khoshnegar, Milad [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of)
2008-02-15
In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh-Taylor instability.
Analytical study of dissipative solitary waves
In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh-Taylor instability
The solitary electromagnetic waves in the graphene superlattice
d’Alembert equation written for the electromagnetic waves propagating in the graphene superlattice is analyzed. The possibility of the propagation of the solitary electromagnetic waves in the graphene superlattice is discussed. The amplitude and the width of the electromagnetic pulse are calculated. The drag current induced by such wave across the superlattice axis is investigated. The numerical estimate of the charge dragged by the solitary wave is made.
Deep-water internal solitary waves near critical density ratio
Agafontsev, D S; Kuznetsov, E A
2005-01-01
Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the supercritical bifurcation changes to the subcritical one. As the solitary wave velocity approaches the minimum phase velocity of linear interfacial waves (the bifurcation point), the solitary wave solutions transform into envelope solitons. In order to describe their behavior and bifurcations, a generalized nonlinear Schr\\"{o}dinger equation describing the behavior of solitons and their bifurcations is derived. In comparison with the classical NLS equation this equation takes into account three additional nonlinear terms: the so-called Lifshitz term responsible for pulse steepening, a nonlocal term analogous to that first found by Dysthe for gravity waves and the six-wave interaction term. We study both analytically and numerically two solitary wave families of this equation for va...
Acoustics waves and oscillations
Sen, S.N.
2013-01-01
Parameters of acoustics presented in a logical and lucid style Physical principles discussed with mathematical formulations Importance of ultrasonic waves highlighted Dispersion of ultrasonic waves in viscous liquids explained This book presents the theory of waves and oscillations and various applications of acoustics in a logical and simple form. The physical principles have been explained with necessary mathematical formulation and supported by experimental layout wherever possible. Incorporating the classical view point all aspects of acoustic waves and oscillations have been discussed together with detailed elaboration of modern technological applications of sound. A separate chapter on ultrasonics emphasizes the importance of this branch of science in fundamental and applied research. In this edition a new chapter ''Hypersonic Velocity in Viscous Liquids as revealed from Brillouin Spectra'' has been added. The book is expected to present to its readers a comprehensive presentation of the subject matter...
Mandal, Debraj; Sharma, Devendra [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2014-10-15
The finite amplitude ion acoustic waves that trap electrons modify the structure of the evolving nonlinear soliton solutions. In the numerical simulations, self-consistently generated solitary waves are studied that emerge as a result of a current driven microinstability growing the ion acoustic mode in a collisionless Vlasov plasma. The growth saturates as a result of nonlinear effects governed by a combination of nonlinearities originating from the hydrodynamic model and kinetic particle trapping effects. The resulting solitary waves also coexist with a finite current and an electron plasma wave capable of perturbing the trapping potential. The results of multiscale simulation are analyzed and characterized following the kinetic prescription of undamped trapped particle mode in the form of phase space vortex solutions that are generalized form of Sagdeev's solitons and obey the solutions of a modified Korteweg-de Vries equation, accounting for a stronger nonlinearity originating from the electron trapping.
Electromagnetic solitary waves in magnetized plasmas
A Hamiltonian formulation, in terms of noncanonical Poisson bracket, is presented for a nonlinear fluid system that includes reduced magnetohydrodynamics and the Hasegawa-Mima equation as limiting cases. The single-helicity and axisymmetric versions possess three nonlinear Casimir invariants, from which a generalized potential can be constructed. Variation of the generalized potential yields a description of exact nonlinear stationary states. The new equilibria, allowing for plasma flow as well as partial electron adiabaticity, are distinct from those found in conventional magnetohydrodynamic theory. They differ from electrostatic stationary states in containing plasma current and magnetic field excitation. One class of steady-state solutions is shown to provide a simple electromagnetic generalization of drift-solitary waves
Efficient computation of capillary-gravity generalized solitary waves
Dutykh, Denys; Duran, Angel
2015-01-01
This paper is devoted to the computation of capillary-gravity solitary waves of the irrotational incompressible Euler equations with free surface. The numerical study is a continuation of a previous work in several points: an alternative formulation of the Babenko-type equation for the wave profiles, a detailed description of both the numerical resolution and the analysis of the internal flow structure under a solitary wave. The numerical code used in this study is provided in open source for interested readers.
Planar and Nonplanar Solitary Waves in a Four-Component Relativistic Degenerate Dense Plasma
M. R. Hossen
2014-01-01
degenerate electrons, nonrelativistic degenerate ions, and arbitrarily charged static heavy ions has been investigated theoretically. The Korteweg-de Vries (K-dV equation has been derived by employing the reductive perturbation method. Their solitary wave solution is obtained and numerically analyzed in case of both planar and nonplanar (cylindrical and spherical geometry. It has been observed that the ion-acoustic (IA and modified ion-acoustic (mIA solitary waves have been significantly changed due to the effects of degenerate plasma pressure and number densities of the arbitrarily charged heavy ions. It has been also found that properties of planar K-dV solitons are quite different from those of nonplanar K-dV solitons. There are numerous variations in case of mIA solitary waves due to the polarity of heavy ions. The basic features and the underlying physics of IA and mIA solitary waves, which are relevant to some astrophysical compact objects, are briefly discussed.
A plethora of generalised solitary gravity-capillary water waves
Clamond, Didier; Duran, Angel
2014-01-01
The present study describes, first, an efficient algorithm for computing gravity-capillary solitary waves solutions of the irrotational Euler equations and, second, provides numerical evidences of the existence of (likely) an infinite number of generalised solitary waves (i.e. solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain (which is to be determined) is mapped into a uniform strip of the complex plane. A Babenko-like equation is then derived from a Lagrangian expressed in the transformed domain. The Babenko equation is then solved numerically using a Levenberg-Marquardt algorithm. Various interesting solutions are computed, some of them being known, some seem to be new. The emergence of generalised solitary waves is shown when the Bond number is increased.
Solitary waves in twist-opening models of DNA dynamics
Gaeta, Giuseppe; Venier, Laura
2008-07-01
We analyze traveling solitary wave solutions in the Barbi-Cocco-Peyrard twist-opening model of nonlinear DNA dynamics. We identify conditions, involving an interplay of physical parameters and asymptotic behavior, for such solutions to exist, and provide first-order ordinary differential equations whose solutions give the required solitary waves; these are not solvable in analytical terms, but are easily integrated numerically. The conditions for existence of solitary waves are not satisfied for trivial asymptotic behavior and physical values of the parameters, i.e., the Barbi-Cocco-Peyrard model admits only solitary wave solutions that entail a global modification of the molecule; this is compared with the situation met in another recently formulated class of DNA models with two degrees of freedom per site.
Multiscale tunability of solitary wave dynamics in tensegrity metamaterials
Fraternali, Fernando; Carpentieri, Gerardo; Amendola, Ada; Skelton, Robert E.; Nesterenko, Vitali F.
2014-01-01
A new class of strongly nonlinear metamaterials based on tensegrity concepts is proposed and the solitary wave dynamics under impact loading is investigated. Such systems can be tuned into elastic hardening or elastic softening regimes by adjusting local and global prestress. In the softening regime these metamaterials are able to transform initially compression pulse into a solitary rarefaction wave followed by oscillatory tail with progressively decreasing amplitude. Interaction of a compre...
Solitary wave propagation in surface stabilized ferroelectric liquid crystal cells
VIJ, JAGDISH; Song, Jang-Kun
2008-01-01
PUBLISHED Solitary wave propagation in surface stabilized ferroelectric liquid crystal cells controlled by surface anchoring of the alignment layers is investigated for different conditions of alignment on the two opposite surfaces. We show that the critical field Ec, where the speed of the solitary wave becomes zero, is finite for asymmetric alignment on two surfaces. We also show that the polar anchoring energy difference (Deltawp) between the alignment layers can be calculated by measur...
Positive and necklace solitary waves on bounded domains
Fibich, G.; Shpigelman, D.
2016-02-01
We present new solitary wave solutions of the two-dimensional nonlinear Schrödinger equation on bounded domains (such as rectangles, circles, and annuli). These multi-peak "necklace" solitary waves consist of several identical positive profiles ("pearls"), such that adjacent "pearls" have opposite signs. They are stable at low powers, but become unstable at powers well below the critical power for collapse Pcr. This is in contrast with the ground-state ("single-pearl") solitary waves on bounded domains, which are stable at any power below Pcr. On annular domains, the ground state solitary waves are radial at low powers, but undergo a symmetry breaking at a threshold power well below Pcr. As in the case of convex bounded domains, necklace solitary waves on the annulus are stable at low powers and become unstable at powers well below Pcr. Unlike on convex bounded domains, however, necklace solitary waves on the annulus have a second stability regime at powers well above Pcr. For example, when the ratio of the inner to outer radii is 1:2, four-pearl necklaces are stable when their power is between 3.1Pcr and 3.7Pcr. This finding opens the possibility to propagate localized laser beams with substantially more power than was possible until now. The instability of necklace solitary waves is excited by perturbations that break the antisymmetry between adjacent pearls, and is manifested by power transfer between pearls. In particular, necklace instability is unrelated to collapse. In order to compute numerically the profile of necklace solitary waves on bounded domains, we introduce a non-spectral variant of Petviashvili's renormalization method.
Axisymmetric solitary waves on the surface of a ferrofluid
Bourdin, Elise; Bacri, Jean-Claude; Falcon, Eric
2010-01-01
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of ...
Solitary electrostatic waves are possible in unmagnetized symmetric pair plasmas
A possibility of stationary solitary electrostatic waves with large amplitude in symmetric unmagnetized symmetric pair plasmas (e-e+ plasma, C60-C60+ plasma or e-h+ plasma) is proven. The main idea of the work is a thermodynamic unequilibrium of plasma species which may be created in low-density ideal pair plasmas. Ranges of parameters (Mach number M and a nonequilibrium degree τ=T+/T-) which lead to the possibility of solitary waves are found
Stability of solitary wave solutions for equations of short and long dispersive waves
Jaime Angulo Pava
2006-01-01
In this paper, we consider the existence and stability of a novel set of solitary-wave solutions for two models of short and long dispersive waves in a two layer fluid. We prove the existence of solitary waves via the Concentration Compactness Method. We then introduce the sets of solitary waves obtained through our analysis for each model and we show that them are stable provided the associated action is strictly convex. We also establish the existence of intervals of conve...
Shoaling of internal solitary waves at the ASIAEX site in the South China Sea
K. G. Lamb
2014-07-01
Full Text Available The interaction of barotropic tides with Luzon Strait topography generates westward propagating internal bores and solitary waves trains which eventually shoal and dissipate on the western side of the South China Sea. Two-dimensional numerical simulations of this shoaling process at the site of the Asian Seas International Acoustic Experiment (ASIAEX have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry, and to explore the influence of rotation. A range of wave amplitudes are considered. Comparisons with adiabatic shoaling waves are also made and the potential impact of a non-slip boundary condition are briefly explored. On the slope secondary solitary waves and mode-two wave packets are generated which propagate towards the shelf. Comparisons with observations made during the ASIAEX experiment are made.
Kazantseva E.V.
2015-01-01
Full Text Available In a model which describes asymmetric oppositely directed nonlinear coupler it was observed in numerical simulations a phenomenon of solitary wave generation from the input constant continuous wave set at the entrance of a waveguide with negative refraction. The period of solitary wave formation decreases with increase of the continuum wave amplitude.
On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath
J. S. Pickett
2005-01-01
other waves and electrostatic fluctuations in this region making it impossible to isolate or clearly distinguish them from these other emissions in the waveform data. Based on these results, we have concluded that some of the near-Earth magnetosheath solitary waves, perhaps in the form of electron phase-space holes, may be generated locally by a two-stream instability involving electrons based on the counterstreaming electrons that are often observed when solitary waves are present. We have not ruled out the possibility that the solitary waves could be generated as a result of the lower-hybrid Buneman instability in the presence of an electron beam, through the electron acoustic mode or through processes involving turbulence, which is almost always present in the magnetosheath, but these will be examined in a more comprehensive study in the future.
Gokhberg, M. B.
1983-07-01
Experiments devoted to acoustic action on the atmosphere-magnetosphere-ionosphere system using ground based strong explosions are reviewed. The propagation of acoustic waves was observed by ground observations over 2000 km in horizontal direction and to an altitude of 200 km. Magnetic variations up to 100 nT were detected by ARIEL-3 satellite near the epicenter of the explosion connected with the formation of strong field aligned currents in the magnetosphere. The enhancement of VLF emission at 800 km altitude is observed.
Multi-valued solitary waves in multidimensional soliton systems
Zheng Chun-Long; Chen Li-Qun; Zhang Jie-Fang
2004-01-01
Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant(2+1)-dimensional soliton systems like the generalized Ablowitz-Kaup-Newell-Segur (GAKNS) model, the generalized Nizhnik-Novikov-Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations.
Diffractons: Solitary Waves Created by Diffraction in Periodic Media
Ketcheson, David I.
2015-03-31
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically varying sound speed. They share some properties with known classes of solitary waves but possess important differences as well.
Banerjee, Gadadhar; Maitra, Sarit [Department of Mathematics, National Institute of Technology Durgapur, Durgapur (India)
2015-04-15
Sagdeev's pseudopotential method is used to study small as well as arbitrary amplitude dust acoustic solitons in a dusty plasma with kappa distributed electrons and ions with dust grains having power law size distribution. The existence of potential well solitons has been shown for suitable parametric region. The criterion for existence of soliton is derived in terms of upper and lower limit for Mach numbers. The numerical results show that the size distribution can affect the existence as well as the propagation characteristics of the dust acoustic solitons. The effect of kappa distribution is also highlighted.
Sagdeev's pseudopotential method is used to study small as well as arbitrary amplitude dust acoustic solitons in a dusty plasma with kappa distributed electrons and ions with dust grains having power law size distribution. The existence of potential well solitons has been shown for suitable parametric region. The criterion for existence of soliton is derived in terms of upper and lower limit for Mach numbers. The numerical results show that the size distribution can affect the existence as well as the propagation characteristics of the dust acoustic solitons. The effect of kappa distribution is also highlighted
S N Paul; S Chattopadhyaya; S K Bhattacharya; B Bera
2003-06-01
Using the pseudopotential method, theoretical investigation has been made on the ﬁrst-order Korteweg-deVries ion-acoustic solitons in a multicomponent plasma consisting of warm positive ions, negative ions and isothermal electrons. The effects of electron-inertia and drift motion of the ions on the amplitudes and widths of the solitons have been studied in a plasma having (H+, Cl-), (H+, O-), (He+, H-) and (He+, O-) ions. Ion-acoustic double-layers have also been investigated for such plasmas. It has been found that drift velocity and electron-inertia have signiﬁcant contribution on the formation of double-layers in multicomponent plasma.
Shoaling of internal solitary waves at the ASIAEX site in the South China Sea
Warn-Varnas, A.; Lamb, K.
2012-04-01
The interaction of barotropic tides with Luzon Strait topography generates westward propagating internal bores and solitary waves trains which eventually shoal and dissipate on the western side of the South China Sea. Numerical simulations of this shoaling process at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process on a variety of environmental factors. The model parameters of the Luzon Strait region are tuned to yield solitary wave trains similar to those observed in the ASIAEX experiments. The sensitivity to details of the stratification, bathymetry, deep water depth and initial wave amplitude as well as the effects of dissipation in a bottom boundary layer are considered. On the slope secondary solitary waves are generated which propagate towards the shelf. In the vicinity of the shelf break a leading square-shaped wave of depression forms which is followed by a series of square-shaped waves of elevation in inviscid simulation. The presence of a bottom boundary significantly modifies the waves trailing the leading depression resulting in the emergence of many more smaller waves. Comparison against the measurements of Orr and Mignerey (2003) are conducted.
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel
2013-07-14
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Axisymmetric solitary waves on the surface of a ferrofluid
Bourdin, Elise; Falcon, Eric
2010-01-01
We report the first observation of axisymmetric solitary waves on the surface of a cylindrical magnetic fluid layer surrounding a current-carrying metallic tube. According to the ratio between the magnetic and capillary forces, both elevation and depression solitary waves are observed with profiles in good agreement with theoretical predictions based on the magnetic analogue of the Korteweg-deVries equation. We also report the first measurements of the velocity and the dispersion relation of axisymmetric linear waves propagating on the cylindrical ferrofluid layer that are found in good agreement with theoretical predictions.
Dühring, Maria Bayard
The work of this project is concerned with the simulation of surface acoustic waves (SAW) and topology optimization of SAW devices. SAWs are elastic vibrations that propagate along a material surface and are extensively used in electromechanical filters and resonators in telecommunication. A new...... application is modulation of optical waves in waveguides. This presentation elaborates on how a SAW is generated by interdigital transducers using a 2D model of a piezoelectric, inhomogeneous material implemented in the high-level programming language Comsol Multiphysics. The SAW is send through a model of a...... output waveguide and the MZI can thus be used as an optical switch. It is explained how the mechanical model of the SAW is coupled to a model of the optical waves such that the change in effective refractive index introduced in the MZI arms by the SAW can be calculated. Results of a parameter study of...
Solitary Wave in Linear ODE with Variable Coefficients
LIU Shi-Da; FU Zun-Tao; LIU Shi-Kuo; XIN Guo-Jun; LIANG Fu-Ming; FENG Bei-Ye
2003-01-01
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.
Relativistic solitary waves modulating long laser pulses in plasmas
Sánchez-Arriaga, G.; Siminos, E.; Lefebvre, E.
2011-01-01
This article discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From the mathematical point of view they are exact solutions of the 1-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of traveling wave solutions with velocity $V$ and vector potential frequency $\\omega$, the fluid m...
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Yang, Jinkyu; Silvestro, Claudio; Sangiorgio, Sophia N.; Borkowski, Sean L.; Ebramzadeh, Edward; De Nardo, Luigi; Daraio, Chiara
2012-01-01
We propose a new biomedical sensing technique based on highly nonlinear solitary waves to assess orthopaedic implant stability in a nondestructive and efficient manner. We assemble a granular crystal actuator consisting of a one-dimensional tightly packed array of spherical particles, to generate acoustic solitary waves. Via direct contact with the specimen, we inject acoustic solitary waves into a biomedical prosthesis, and we nondestructively evaluate the mechanical integrity of the bone-prosthesis interface, studying the properties of the waves reflected from the contact zone between the granular crystal and the implant. The granular crystal contains a piezoelectric sensor to measure the travelling solitary waves, which allows it to function also as a sensor. We perform a feasibility study using total hip arthroplasty (THA) samples made of metallic stems implanted in artificial composite femurs using polymethylmethacrylate for fixation. We first evaluate the sensitivity of the proposed granular crystal sensor to various levels of prosthesis insertion into the composite femur. Then, we impose a sequence of harsh mechanical loading on the THA samples to degrade the mechanical integrity at the stem-cement interfaces, using a femoral load simulator that simulates aggressive, accelerated physiological loading. We investigate the implant stability via the granular crystal sensor-actuator during testing. Preliminary results suggest that the reflected waves respond sensitively to the degree of implant fixation. In particular, the granular crystal sensor-actuator successfully detects implant loosening at the stem-cement interface following violent cyclic loading. This study suggests that the granular crystal sensor and actuator has the potential to detect metal-cement defects in a nondestructive manner for orthopaedic applications.
Relativistic solitary waves modulating long laser pulses in plasmas
Sanchez-Arriaga, G; Siminos, E; Lefebvre, E, E-mail: erik.lefebvre@cea.fr [CEA, DAM, DIF, 91297 Arpajon (France)
2011-04-15
This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency {omega}, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V-{omega} plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.
NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP
LU Ji; YU Xi-ping
2008-01-01
Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.
Exact solitary wave solutions of nonlinear wave equations
ZHANG; Guixu
2001-01-01
［1］Ablowitz, M.J., Carkson, P.A., Nonlinear Evolution and Inverse Scattering., New York: Cambridge University Press, 1991, 47-350.［2］Miura, M.R., Bcklund Transformation, Berlin: Springer_Verlag, 1978, 4-156.［3］Hirota, R., Exact solution of the Korteweg_de Vries equation for multiple collisions of solitons, Phys.Rev.Lett., 1971, 27: 1192-1194.［4］Wang, M.L., Zhou, Y.B., Li, Z.B., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys.Lett.A, 1996, 213: 67-75.［5］Shang, Y.D., Explicit and exact solutions for a class of nonlinear wave equations, Acta Appl.Math.Sinica (in Chinese), 2000, 23(1): 21-30.［6］Li, Z.B., Zhang, S.Q., Exact solitary wave equations for nonlinear wave equations using symbolic computation, Acta Math.Phys.Sinica (in Chinese), 1997, 17(1): 81-89.［7］Wu Wenjun, On zeros of algebraic equations: An application of Ritt principle, Kexue Tongbao (Chinese Science Bulletin), 1986, 31(1): 1-5.［8］Heegard, C., Little, J., Saints, K., Systematic encoding via grbner bases fro a class of algebraic geometric codes, IEEE Trans.Inform.Theory, 1995, IT_41: 1752-1761.［9］Conte, R., Musette, M., Link between solitary waves and projective Riccati equation, J.Phys.A: Math.Gen., 1992, 25: 2609-2612.［10］Wahlquist, H.D., Estabrook, F.B., Prolongation structures and nonlinear evolution equations, J.Math.Phys., 1975, 16: 1-7.［11］Whitham, G.B., Linear and Nonlinear Waves, New York: Wiley, 1974, 44.［12］Constantin, P., Foias, C., Nicolaenko, B., Integral Manifolds and Inertial Manifolds for Dissipative Partial Differtial Equations, New York: Springer_Verlag, 1981, 111-118.［13］Chen, S.R., Chen, X.J., Completeness relation of squared Jost functions to the NLS equation, Acta Phys.Sinica (in Chinese), 1999, 48(5): 882-886.
Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation
Bao-Feng Feng
2005-01-01
based on the phase plane analysis around the equilibrium point, is used to construct the solitary-wave solutions for this nonintegrable equation. A symmetric three-level implicit finite difference scheme with a free parameter θ is proposed to study the propagation and interactions of solitary waves. Numerical simulations show the propagation of a single solitary wave of SGBE, and two solitary waves pass by each other without changing their shapes in the head-on collisions.
Singh, Manpreet; Singh Saini, Nareshpal; Ghai, Yashika; Kaur, Nimardeep
2016-07-01
Dusty plasma is a fully or partially ionized gas which contain micron or sub-micron sized dust particles. These dust particles can be positively or negatively charged, depending upon the mechanism of charging . Dusty plasma is often observed in most of the space and astrophysical plasma environments. Presence of these dust particles can modify the dispersion properties of waves in the plasma and can introduce several new wave modes, e.g., dust acoustic (DA) waves, dust-ion acoustic (DIA) waves, dust-acoustic shock waves etc. In this investigation we have studied the small amplitude dust acoustic waves in an unmagnetized plasma comprising of electrons, positively charged ions, negatively charged hot as well as cold dust. Electrons and ions are described by superthermal distribution which is more appropriate for modeling space and astrophysical plasmas. Kadomtsev- Petviashvili (KP) equation has been derived using reductive perturbation technique. Positive as well as negative potential structures are observed, depending upon some critical values of parameters. Amplitude and width of dust acoustic solitary waves are modified by varying these parameters such as superthermality of electrons and ions, direction of propagation of the wave, relative concentration of hot and cold dust particles etc. This study may be helpful in understanding the formation and dynamics of nonlinear structures in various space and astrophysical plasma environments such Saturn's F-rings.
Existence of solitary travelling waves in interfacial electrohydrodynamics
Hammerton, Paul
2013-01-01
The propagation of waves on the surface of a fluid layer of finite depth is considered in the presence of a normal electric field, due to parallel electrodes at arbitrary separation distance. The combined effect of electric field, gravity and surface tension is considered in the long-wavelength small-amplitude limit. Travelling wave solutions are characterised in terms of the Froude number, an electric Weber number and a Bond number and conditions for the existence of solitary waves are deter...
Single-peak solitary wave solutions for the variant Boussinesq equations
Hong Li; Lilin Ma; Dahe Feng
2013-06-01
This paper presents all possible smooth, cusped solitary wave solutions for the variant Boussinesq equations under the inhomogeneous boundary condition. The parametric conditions for the existence of smooth, cusped solitary wave solutions are given using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for smooth, cusped solitary wave solutions of the variant Boussinesq equations.
Stability of solitary wave solutions for equations of short and long dispersive waves
Jaime Angulo Pava
2006-07-01
Full Text Available In this paper, we consider the existence and stability of a novel set of solitary-wave solutions for two models of short and long dispersive waves in a two layer fluid. We prove the existence of solitary waves via the Concentration Compactness Method. We then introduce the sets of solitary waves obtained through our analysis for each model and we show that them are stable provided the associated action is strictly convex. We also establish the existence of intervals of convexity for each associated action. Our analysis does not depend of spectral conditions.
Flow and sediment transport induced by a plunging solitary wave
Sumer, B. Mutlu; Sen, M.Berke; Karagali, Ioanna;
2011-01-01
Two parallel experiments involving the evolution and runup of plunging solitary waves on a sloping bed were conducted: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses, and (2) a sediment-bed experiment, allowing for the measurement of pore-water pressures...
No solitary waves exist on 2D deep water
The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water under the influence of gravity is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to show that it admits no solutions which asymptotically vanish faster than linearly. (paper)
Numerical simulations of Klein-Gordon solitary-wave interactions
Solitons of a non-linear Klein-Gordon equation are studied numerically using a cubic B-spline finite-element method. Test results indicate that, when solitary waves interact, the final state obtained depends on their relative velocity.The simulations confirm existing observations and produce new results. The numerical algorithm developed is efficient with an undemanding stability criterion
Nonpropagating Solitary Waves in (2+1)-Dimensional Nonlinear Systems
MENG Jian-Ping; ZHANG Jie-Fang
2005-01-01
By means of extended homogeneous balance method and variable separation approach, quite a general variable separation solution of the (2+1)-dimensional Broer-Kaup-Kupershmidt equation is derived. From the variable separation solution and by selecting appropriate functions, a new class of (2+1)-dimensional nonpropagating solitary waves are found. The novel features exhibited by these new structures are first revealed.
Experiments and computation of onshore breaking solitary waves
Jensen, A.; Mayer, Stefan; Pedersen, G.K.
2005-01-01
This is a combined experimental and computational study of solitary waves that break on-shore. Velocities and accelerations are measured by a two-camera PIV technique and compared to theoretical values from an Euler model with a VOF method for the free surface. In particular, the dynamics of a so...
No solitary waves exist on 2D deep water
Hur, Vera Mikyoung
2015-01-01
The solitary wave problem at the free surface of a two-dimensional, infinitely-deep and irrotational flow of water, under the influence of gravity, is formulated as a nonlinear pseudodifferential equation. A Pohozaev identity is used to show that it admits no solutions which asymptotically vanish faster than linearly.
Internal solitary waves in the Red Sea: An unfolding mystery
da Silva, J.C.B.; Magalhães, J.M.; Gerkema, T.; Maas, L.R.M.
2012-01-01
The off-shelf region between 16.0 degrees and 16.5 degrees N in the southern Red Sea is identified as a new hotspot for the occurrence of oceanic internal solitary waves. Satellite observations reveal trains of solitons that, surprisingly, appear to propagate from the center of the Red Sea, where it
Grey Self-similar Solitary Waves in Inhomogeneous Nonlinear Media
LI Hua-Mei
2009-01-01
This paper analyzes spatial grey self-similar solitary waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities.New exact self-similar solutions are found using a novel transformation and their main features are investigated by using direct computer simulations.
Dynamics of Gravity-Capillary Solitary Waves in Deep Water
Wang, Zhan; Milewski, Paul A.
2012-01-01
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential flow problem by taking a cubic truncation of the scaled Dirichlet-to-Neumann operator for the normal velocity on the free surface. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of ...
Solitary and periodic waves in two-fluid magnetohydrodynamics
Gavrikov, M. B.; Kudryashov, N. A.; Petrov, B. A.; Savelyev, V. V.; Sinelshchikov, D. I.
2016-09-01
A system of equations of two-fluid magnetohydrodynamics is studied. An ordinary differential equation describing traveling waves in an ideal cold quasi-neutral plasma is obtained in the case of quasi-stationary electromagnetic field. The Painlevé analysis of this equation is carried out and the general solution of the equation is constructed in terms of the Weierstrass elliptic function. Solitary and periodic wave solutions for the components of magnetic field are found and analyzed.
Existence of solitary waves in dipolar quantum gases
Antonelli, Paolo
2011-02-01
We study a nonlinear Schrdinger equation arising in the mean field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some of their properties. This gives a rigorous argument for the possible existence of solitary waves in BoseEinstein condensates, which originate solely due to the dipolar interaction between the particles. © 2010 Elsevier B.V. All rights reserved.
Energetics of internal solitary waves in a background sheared current
K. G. Lamb
2010-10-01
Full Text Available The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.
Solitary wave shoaling and breaking in a regularized Boussinesq system
Senthilkumar, Amutha
2016-01-01
A coupled BBM system of equations is studied in the situation of water waves propagating over decreasing fluid depth. A conservation equation for mass and a wave breaking criterion valid in the Boussinesq approximation is found. A Fourier collocation method coupled with a 4-stage Runge-Kutta time integration scheme is employed to approximate solutions of the BBM system. The mass conservation equation is used to quantify the role of reflection in the shoaling of solitary waves on a sloping bottom. Shoaling results based on an adiabatic approximation are analyzed. Wave shoaling and the criterion of breaking solitary waves on a sloping bottom is studied. To validate the numerical model the simulation results are compared with those obtained by Grilli et al.[16] and a good agreement between them is observed. Shoaling of solitary waves of two different types of mild slope model systems in [8] and [13] are compared, and it is found that each of these models works well in their respective regimes of applicability.
Electron-acoustic solitary pulses and double layers in multi-component plasmas
Mannan, A; Shukla, P K
2013-01-01
We consider the nonlinear propagation of fi?nite amplitude electron-acoustic waves (EAWs) in multi-component plasmas composed of two distinct groups of electrons (cold and hot components), and non-isothermal ions. We use the continuity and momentum equations for cold inertial electrons, Boltzmann law for inertialess hot electrons, non-isothermal density distribution for hot ions, and Poisson's equation to derive an energy integral with a modi?ed Sagdeev potential (MSP) for nonlinear EAWs. The MSP is analyzed to demonstrate the existence of arbitrary amplitude EA solitary pulses (EASPs) and EA double layers (EA-DLs). Small amplitude limits have also been considered and analytical results for EASPs and EA-DLs are presented. The implication of our results to space and laboratory plasmas is briely discussed.
Salient features of solitary waves in dusty plasma under the influence of Coriolis force
The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variation caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons
On the energetic stability of solitary water waves.
Mielke, Alexander
2002-10-15
We study solutions of the water-wave problem for a fluid layer of finite depth in the presence of gravity and surface tension. We use the canonical Hamiltonian formulation by Zakharov in terms of the surface elevation and the trace of the velocity potential on the surface. With a new continuity result for the Dirichlet-Neumann operator in terms of the surface as a function in H(1)(R), we show conditional energetic stability of the trivial solution in certain regions of the parameter space. In the same region we obtain stability of solitary waves under the additional assumption that the second variation of the energy has only one negative eigenvalue. The latter assumption is shown to be fulfilled for the small-amplitude solitary waves first constructed by Amick & Kirchgässner. PMID:12804235
Electron acoustic waves in a magnetized plasma with kappa distributed ions
Devanandhan, S.; Lakhina, G. S. [Indian Institute of Geomagnetism, Navi Mumbai (India); Singh, S. V. [Indian Institute of Geomagnetism, Navi Mumbai (India); School of Physics, University of Kwazulu-Natal, Durban (South Africa); Bharuthram, R. [University of the Western Cape, Bellville (South Africa)
2012-08-15
Electron acoustic solitary waves in a two component magnetized plasma consisting of fluid cold electrons and hot superthermal ions are considered. The linear dispersion relation for electron acoustic waves is derived. In the nonlinear regime, the energy integral is obtained by a Sagdeev pseudopotential analysis, which predicts negative solitary potential structures. The effects of superthermality, obliquity, temperature, and Mach number on solitary structures are studied in detail. The results show that the superthermal index {kappa} and electron to ion temperature ratio {sigma} alters the regime where solitary waves can exist. It is found that an increase in magnetic field value results in an enhancement of soliton electric field amplitude and a reduction in soliton width and pulse duration.
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel [Plasma Physics Group, Faculty of Sciences-Physics, Theoretical Physics Laboratory, University of Bab-Ezzouar, USTHB BP 32, El Alia, Algiers 16111 (Algeria)], E-mail: mtribeche@usthb.dz
2009-09-15
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Measurement and modelling of bed shear induced by solitary waves
JayaKumar, S.
±20% accuracy, which is probably adequate for most practical engineering purposes. 168 Solitary wave induced shear stresses Chapter 10: Conclusions 10.3. Friction factors The wave friction factors derived from the classical drag law vary... Engineering, 56(5-6): 506-516. Baldock, T.E. and Holmes, P., 1998. Seepage effects on sediment transport by waves and currents. 26th International Conference Coastal Engineering, Orlando, p.^pp. 3601- 3614. Barends, F.B.J. and Spierenburg, S.E.J., 1991...
A solitary wave of a relativistic magnetosonic wave propagating perpendicularly to a magnetic field
A relativistic theory for a nonlinear magnetosonic wave propagating perpendicularly to a magnetic field is developed. On the basis of a relativistic two-fluid cold plasma model, structure of a stationary magnetosonic wave is studied. Relativistic effects become important for the parameter regime ωce/ωpe > approx 1, because the fluid electron velocity perpendicular to a magnetic field and parallel to the wave front takes values close to the speed of light for such plasma parameters. It is found that there exists a stationary solitary wave solution even in the relativistic model. Some properties of the solitary wave, such as the soliton width, are discussed. (author)
Solitary Waves Observed By Cluster In the Solar Wind
Fraenz, M.; Horbury, T. S.; Génot, Vincent; Moullard, O.; Rème, Henri; Dandouras, I.; Fazakerley, A. N.; A. Korth; Frutos-Alfaro, F.
2003-01-01
Short dropouts of the magnetic field intensity have been frequently observed in the solar wind on interplanetary spacecraft. But so far it could not be established whether these are caused by kinetic instabilities or whether they can be described as solitary MHD waves. The multi-satellite observations of the Cluster-mission allow for the first time to measure proton and electron distributions with a sufficient temporal and spatial resolution to tackle this question. We use measurements by the...
Airy-type solitary wave in highly noninstantaneous Kerr media.
Deng, Fu; Hong, Weiyi; Deng, Dongmei
2016-07-11
We investigate the dynamics of a decelerating Airy pulse in the highly noninstantaneous Kerr media. It is found that the deceleration of the Airy pulse can be counteracted by the highly noninstantaneous nonlinearity. When the power of the pulse is specifically chosen, the deceleration of the Airy pulse can be totally restrained, and an Airy-type solitary wave is observed within several dispersion lengths. PMID:27410868
Hydrodynamics of the Solitary Waves Travelling Down a Liquid
Tihon, Jaroslav
Reihe 3, č. 817 (2004), s. 260-269. ISSN 0178-9503. [International Berlin Workshop-IBW2 on Transport Phenomena with Moving Boundaries /2./. Berlin, 09.11.2003-10.11.2003] R&D Projects: GA MŠk OC F2.10 Institutional research plan: CEZ:AV0Z4072921 Keywords : wavy film flow * solitary waves * electrodiffusion technique Subject RIV: CI - Industrial Chemistry, Chemical Engineering
Dynamics of solitary waves in the Zakharov model equations
We analyze internal vibrations of a solitary wave in the generalized Zakharov system (including a direct nonlinear self-interaction of the high-frequency field) by means of a variational approach. The application of the variational approximation to this model turns out to be nontrivial, as one needs to renormalize the Lagrangian in order to avoid divergences. This is done with the use of two fundamental integrals of motion of the model. We derive a Hamiltonian two-degrees-of-freedom dynamical system that governs internal vibrations of the solitary wave. The eigenfrequencies of the small oscillations around the unperturbed solitary wave are found explicitly, one of them lying inside the gap of the high-frequency subsystem, the other one being well above the gap. Finite-amplitude oscillations are simulated numerically. It is shown that these oscillations remain regular if the perturbation does not break the balance between the two integrals of motion, while in the opposite case the oscillations are more irregular and may possibly become chaotic. copyright 1997 The American Physical Society
Weakly nonlinear models for internal waves: inverse scattering transform and solitary wave contents
Chen, Shengqian
2016-01-01
The time evolution emanating from ``internal dam-break'' initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical simulations and experiments in wave tanks show that such initial conditions eventually give rise to coherent structures that are close to solitary-wave solutions moving ahead of a region of dispersive wave motion and turbulent mixing close to the location of the initial dam step. A priori theoretical predictions of the main features of these solitary waves, such as their amplitudes and speeds, appear to be unavailable, even for simplified models of wave evolution in stratified fluids. With the aim of providing estimates of the existence, amplitude and speed of such solitary waves, an approach based on Inverse Scattering Transform (IST) for completely integrable models is developed here and tested against direct numerical simulations of Euler fluids and some of their mode...
Lamb, K. G.; Warn-Varnas, A.
2015-05-01
The interaction of barotropic tides with Luzon Strait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Two-dimensional numerical simulations of the shoaling of a single internal solitary wave at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry and to explore the influence of rotation. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200-300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50% larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer
Hong-Yan Wang; Kai-Biao Zhang
2015-01-01
Propagation of small but finite nonlinear dust-acoustic solitary waves are investigated in a planar unmagnetized dusty plasma, which consists of electrons, positrons, ions and negatively charged dust particles with different sizes and masses. A Kadomtsev–Petviashvili (KP) equation is obtained by using reductive perturbation method. The effect of positron density and positron–electron temperature ratio on dust-acoustic solitary structures are studied. Numerical results show that the increase in positron number density increases the amplitude of hump-like solitons but decreases the dip-like solitary waves. Furthermore, increase in the positron–electron temperature ratio results in the decrease of the amplitude of dip-like solitary waves. It seems that both the dipand hump-like solitary waves can exist in this system. Our results also suggest that the dust-size distribution has a significant role on the amplitude of the solitary waves.
Propagation of small but finite nonlinear dust-acoustic solitary waves are investigated in a planar unmagnetized dusty plasma, which consists of electrons, positrons, ions and negatively charged dust particles with different sizes and masses. A Kadomtsev-Petviashvili (KP) equation is obtained by using reductive perturbation method. The effect of positron density and positron- electron temperature ratio on dust-acoustic solitary structures are studied. Numerical results show that the increase in positron number density increases the amplitude of hump-like solitons but decreases the dip-like solitary waves. Furthermore, increase in the positron-electron temperature ratio results in the decrease of the amplitude of dip-like solitary waves. It seems that both the dip and hump-like solitary waves can exist in this system. Our results also suggest that the dust-size distribution has a significant role on the amplitude of the solitary waves. (author)
CHENYong; YANZhen－Ya; 等
2002-01-01
In this paper,we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method.As a result,many explicit exact solutions,which contain new solitary wave solutions,periodic wave solutions,and the combined formal solitary wave solutions,and periodic wave solutions ,are obtained.
On the three-dimensional configuration of electrostatic solitary waves
V. L. Krasovsky
2004-01-01
Full Text Available The simplest models of the electrostatic solitary waves observed by the Geotail spacecraft in the magnetosphere are developed proceeding from the concept of electron phase space holes. The technique to construct the models is based on an approximate quasi-one-dimensional description of the electron dynamics and three-dimensional analysis of the electrostatic structure of the localized wave perturbations. It is shown that the Vlasov-Poisson set of equations admits a wide diversity of model solutions of different geometry, including spatial configurations of the electrostatic potential similar to those revealed by Geotail and other spacecraft in space plasmas.
The Froude number for solitary water waves with vorticity
Wheeler, Miles H.
2014-01-01
We consider two-dimensional solitary water waves on a shear flow with an arbitrary distribution of vorticity. Assuming that the horizontal velocity in the fluid never exceeds the wave speed and that the free surface lies everywhere above its asymptotic level, we give a very simple proof that a suitably defined Froude number $F$ must be strictly greater than the critical value $F=1$. We also prove a related upper bound on $F$, and hence on the amplitude, under more restrictive assumptions on t...
Small amplitude solitary waves in the Dirac-Maxwell system
Comech, Andrew; Stuart, David
2012-01-01
We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\\phi(x,\\omega)e^{-i\\omega t}$, $\\omega\\in(-m,\\omega_*)$, with some $\\omega_*>-m$, such that $\\phi_\\omega\\in H^1(\\R^3,\\C^4)$, $\\Vert\\phi_\\omega\\Vert^2_{L^2}=O(m-|\\omega|)$, and $\\Vert\\phi_\\omega\\Vert_{L^\\infty}=O(m-|\\omega|)$. The method of proof is an implicit function theorem argument based on an identification of the nonrelativis...
Rotating solitary wave at the wall of a cylindrical container
Amaouche, Mustapha
2013-04-30
This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg–de Vries equation for the wall wave profile, which did not account for the rotational character of the base flow. The present formulation is based on a less restricting condition and consequently corrects the last shortcoming. Now the influence of the background flow appears in the wave characteristics. The theory provides a better physical depiction of the unique experiment by predicting fairly well the wave profile at least in the first half of its lifetime and estimating the speed of the observed wave with good accuracy.
An experimental study on runup of two solitary waves on plane beaches
XUAN Rui-tao; WU Wei; LIU Hua
2013-01-01
Experiments of the runup of two solitary waves on a plane beach are carried out in a wave flume.The two solitary waves with the same amplitude and the crest separating distances are generated by using an improved wave generation method.It is found that,with regard to the two solitary waves with same wave amplitude,the runup amplification of the second wave is less than that of the first wave if the relative crest separating distance is reduced to a certain threshold value.The rundown of the first solitary wave depresses the maximum runup of the second wave.If the leading solitary wave is of relatively smaller amplitude for the two solitary waves,the runup amplification is affected by the overtaking process of two solitary waves.It turns out that the runup amplification of the second wave is larger than that of the first wave if the similarity factor is approximately larger than 15,which means the larger wave overtakes the smaller one before the waves runup on a beach.
Direct bed stress measurements under solitary tsunami-type waves and breaking tsunami wave fronts
JayaKumar, S.; Baldock, T.E.
, the force measured by the shear plate includes the bed shear stress and the pressure gradient force from the wave. Linear wave theory is often used to estimate (Rankin and Hires, 2000) and eliminate the pressure gradient from the total force so... for selected solitary waves generated in laboratory that are comparable with the theory Parameters Cyclone (shallow) Cyclone (deep) Tsunami-1 (shallow) Tsunami-2 (shallow) Tsunami-1 (deep) Tsunami-2 (deep) Wave height (m) 20 20 1 1 1 1 Wave...
A new model for algebraic Rossby solitary waves in rotation fluid and its solution
Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru
2015-09-01
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
Nonlinear dust-ion-acoustic waves in a multi-ion plasma with trapped electrons
S S Duha; B Shikha; A A Mamun
2011-08-01
A dusty multi-ion plasma system consisting of non-isothermal (trapped) electrons, Maxwellian (isothermal) light positive ions, warm heavy negative ions and extremely massive charge ﬂuctuating stationary dust have been considered. The dust-ion-acoustic solitary and shock waves associated with negative ion dynamics, Maxwellian (isothermal) positive ions, trapped electrons and charge ﬂuctuating stationary dust have been investigated by employing the reductive perturbation method. The basic features of such dust-ion-acoustic solitary and shock waves have been identiﬁed. The implications of our ﬁndings in space and laboratory dusty multi-ion plasmas are discussed.
Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation
Esfahani, Amin
2009-01-01
In this paper we study the generalized BO-ZK equation in two dimensions. We classify the existence and non-existence of solitary waves depending on the sign of the dispersions and on the nonlinearity. By using the approach introduced by Cazenave and Lions we study the nonlinear stability of solitary waves. We also prove some decay and regularity properties of such waves.
Solitary waves of permanent form in a deep fluid with weak shear
Derzho, Oleg G.; Velarde, Manuel G.
1995-06-01
The Benjamin-Davis-Acrivos-Ono equation is generalized to account for finite, large amplitude solitary waves in a sheared deep fluid. It is shown how fine structure of stratification and weak noncritical shear in such geophysical flows do affect length (shape), wave (phase) velocity, and even stability of finite amplitude solitary waves.
ARE PULSING SOLITARY WAVES RUNNING INSIDE THE SUN?
A precise sequence of frequencies—detected four independent ways—is interpreted as a system of solitary waves below the Sun's convective envelope. Six future observational or theoretical tests of this idea are suggested. Wave properties (rotation rates, radial energy distribution, nuclear excitation strength) follow from conventional dynamics of global oscillation modes after assuming a localized nuclear term strong enough to perturb and hold mode longitudes into alignments that form 'families'. To facilitate future tests, more details are derived for a system of two dozen solitary waves 2 ≤ l ≤ 25. Wave excitation by 3He and 14C burning is complex. It spikes by factors M1 ≤ 103 when many waves overlap in longitude but its long-time average is M2 ≤ 10. Including mixing can raise overall excitation to ∼50 times that in a standard solar model. These spikes cause tiny phase shifts that tend to pull wave rotation rates toward their ideal values ∝[l(l + 1)]–1. A system like this would generate some extra nuclear energy in two spots at low latitude on opposite sides of the Sun. Each covers about 20° of longitude. Above a certain wave amplitude, the system starts giving distinctly more nuclear excitation to some waves (e.g., l = 9, 14, and 20) than to neighboring l values. The prominence of l = 20 has already been reported. This transition begins at temperature amplitudes ΔT/T = 0.03 in the solar core for a typical family of modes, which corresponds to δT/T ∼ 0.001 for one of its many component oscillation modes.
On a new type of solitary surface waves in finite water depth
Liao, Shijun
2012-01-01
In this paper, a new type of solitary surface waves in a finite water depth is found by analytically solving the fully nonlinear wave equations. Using a new type of base functions which decays exponentially in the horizontal direction, this new type of solitary surface waves is gained first by means of linear wave equations, and then confirmed by the fully nonlinear wave equations. The new type of solitary surface waves have many unusual characteristics. First, it has a peaked crest. Secondly, it may be in the form of depression, which has been often reported for internal solitary waves but never for free-surface solitary ones, to the best of author's knowledge. Third, its phase speed has nothing to do with wave height. Finally, its horizontal velocity at bottom is always larger than that on surface. All of these are so different from the traditional periodic and solitary waves that they clearly indicate the novelty of the peaked solitary waves. Based on the new peaked solitary surface waves, a new explanatio...
The light filament as vector solitary wave
Kovachev, Lubomir M
2015-01-01
We present an analytical approach to the theory of nonlinear propagation of femtosecond optical pulses with broad-band spectrum in gases. The vector character of the nonlinear third-order polarization is investigated in details, taking into account the carrier to envelope phase. The corresponding system of vector amplitude equations is written by using left-hand and right-hand circular components of the electrical field. We found that this system nonlinear equations admits $3D+1$ vector soliton solution with Lorentz shape. The solution presents relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in plane, orthogonal to the direction of propagation. The evolution of the intensity profile demonstrate weak self-compression and week spherical wave in the first milliseconds of propagation.
Polarized seismic and solitary waves run-up at the sea bed
Dennis, L. C.C.; Zainal, A. A.; Faisal, S. Y. [Universiti Teknologi PETRONAS, 31750 Tronoh, Perak (Malaysia); Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)
2012-09-26
The polarization effects in hydrodynamics are studied. Hydrodynamic equation for the nonlinear wave is used along with the polarized solitary waves and seismic waves act as initial waves. The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. The output demonstrates the inundation behaviors. Consequently, the polarized seismic waves along with the polarized solitary waves tend to generate dissimilar inundation which is more disastrous.
The solitary wave of asexual evolution
Rouzine, Igor M.; Wakeley, John; Coffin, John M.
2003-01-01
Using a previously undescribed approach, we develop an analytic model that predicts whether an asexual population accumulates advantageous or deleterious mutations over time and the rate at which either process occurs. The model considers a large number of linked identical loci, or nucleotide sites; assumes that the selection coefficient per site is much less than the mutation rate per genome; and includes back and compensating mutations. Using analysis and Monte Carlo simulations, we demonstrate the accuracy of our results over almost the entire range of population sizes. Two limiting cases of our results, when either deleterious or advantageous mutations can be neglected, correspond to the Fisher-Muller effect and Muller's ratchet, respectively. By comparing predictions of our model (no recombination) to those of simple single-locus models (strong recombination), we show that the accumulation of advantageous mutations is slowed by linkage over a broad, finite range of population size. This supports the view of Fisher and Muller, who argued in the 1930s that progressive evolution of organisms is slowed because loci at which beneficial mutations can occur are often linked together on the same chromosome. These results follow from our main finding, that distribution of sequences over the mutation number evolves as a traveling wave whose speed and width depend on population size and other parameters. The model explains a logarithmic dependence of steady-state fitness on the population size reported recently for an RNA virus.
On the Synchronization of Acoustic Gravity Waves
Lonngren, Karl E.; Bai, Er-Wei
Using the model proposed by Stenflo, we demonstrate that acoustic gravity waves found in one region of space can be synchronized with acoustic gravity waves found in another region of space using techniques from modern control theory.
Solitonic, periodic and quasiperiodic behaviors of dust ion acoustic waves in superthermal plasmas
The solitonic, periodic, and quasiperiodic behaviors of dust ion acoustic waves in superthermal plasmas with q-nonextensive electrons are studied using the bifurcation theory of planar dynamical systems through direct approach. Using a Galilean transformation, model equations are transformed to a Hamiltonian system involving electrostatic potential. The existence of solitary and periodic waves is shown for the unperturbed Hamiltonian system. Analytical forms of these waves are presented depending on physical parameters q and μ. The effects of q and μ are studied on characteristics of nonlinear dust ion acoustic solitary and periodic waves. It is observed that parameters q and μ significantly influence the characteristics of nonlinear dust ion acoustic solitary and periodic structures. Considering an external periodic perturbation, the quasiperiodic behavior of the perturbed Hamiltonian system for dust ion acoustic waves is studied. It is seen that the unperturbed Hamiltonian system has the solitary and periodic wave solutions whereas the perturbed Hamiltonian system has quasiperiodic motion for same values of parameters q,μ and v. (author)
BGK electron solitary waves: 1D and 3D
L.-J. Chen
2002-01-01
Full Text Available This paper presents new results for 1D BGK electron solitary wave (phase-space electron hole solutions and, based on the new results, extends the solutions to include the 3D electrical interaction (E ~ 1/r 2 of charged particles. Our approach for extending to 3D is to solve the nonlinear 3D Poisson and 1D Vlasov equations based on a key feature of 1D electron hole (EH solutions; the positive core of an EH is screened by electrons trapped inside the potential energy trough. This feature has not been considered in previous studies. We illustrate this key feature using an analytical model and argue that the feature is independent of any specific model. We then construct azimuthally symmetric EH solutions under conditions where electrons are highly field-aligned and ions form a uniform background along the magnetic field. Our results indicate that, for a single humped electric potential, the parallel cut of the perpendicular component of the electric field (E⊥ is unipolar and that of the parallel component (E|| bipolar, reproducing the multi-dimensional features of the solitary waves observed by the FAST satellite. Our analytical solutions presented in this article capture the 3D electric interaction and the observed features of (E|| and E⊥. The solutions predict a dependence of the parallel width-amplitude relation on the perpendicular size of EHs. This dependence can be used in conjunction with experimental data to yield an estimate of the typical perpendicular size of observed EHs; this provides important information on the perpendicular span of the source region as well as on how much electrostatic energy is transported by the solitary waves.
Internal solitary waves in the Red Sea: An unfolding mystery
Da Silva, J. C. B.; Magalhães, J.M.; T. Gerkema; Maas, L.R.M.
2012-01-01
The off-shelf region between 16.0 degrees and 16.5 degrees N in the southern Red Sea is identified as a new hotspot for the occurrence of oceanic internal solitary waves. Satellite observations reveal trains of solitons that, surprisingly, appear to propagate from the center of the Red Sea, where it is deepest, toward the continental shelf, but they do not survive as coherent structures over the shelf. These solitons are characterized by coherent crest lengths exceeding 80 km and crest-to-cre...
Linear Stability of the boundary layer under a solitary wave
Verschaeve, Joris C. G.; Pedersen, Geir K.
2013-01-01
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) reveal- ing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of ...
Measurement and modeling of bed shear stress under solitary waves
Jayakumar, S.; Guard, P.A.; Baldock, T.E.
) of the water particles, and kinematic viscosity (ν ): ν Au R e = (2) In order to estimate R e , the semi-excursion length of the water particles needs to be estimated properly for the solitary waves. This semi-excursion of the water particle... ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ =νν (8) where, z 0 is roughness height, z is depth, ν is kinematic viscosity. It was also shown that to leading order bed shear stress, τ , can be expressed as convolution integral of the depth integrated averaged horizontal velocity, u , Eq...
Nonlinear acoustic-gravity waves
Stenflo, Lennart; Shukla, P. K.
2009-01-01
Previous results on nonlinear acoustic-gravity waves are reconsidered. It turns out that the mathematical techniques used are somewhat similar to those already adopted by the plasma physics community. Consequently, a future interaction between physicists On different fields, e.g in meteorology and plasma physics, can be very fruitful.
A unified intrinsic functional expansion theory for solitary waves
Theodore Yaotsu Wu; John Kao; Jin E. Zhang
2005-01-01
A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F2μπ = tanμπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular inμ), such that 2Mμ is just somewhat beyond unity, i.e. 2Mμ (~-) 1. This fundamental criterion is fully validated by solutions for waves Dedicated to Zhemin Zheng for celebration of his Eightieth Anniversary It gives us a great pleasure to dedicate this study to Prof. Zhemin Zheng and join our distinguished colleagues and friends for the jubilant celebration of his Eightieth Anniversary. Warmest tribute is due from us, as from many others unlimited by borders and boundaries, for his contributions of great significance to science, engineering science and engineering, his tremendous influence as a source of inspiration and unerring guide to countless workers in the field, his admirable leadership in fostering the Institute of Mechanics of world renown, as well as for his untiring endeavor in promoting international interaction and cooperation between academies of various nations
Fukaya, Noriyoshi
2016-01-01
We study the orbital instability of solitary waves for a generalized derivative nonlinear Schr\\"odinger equation. We give sufficient conditions for instability of a two-parameter family of solitary waves in a degenerate case.
Homotopic mapping solitary traveling wave solutions for the disturbed BKK mechanism physical model
Using the trial equation method, a Broer—Kau—Kupershmidt (BKK) mechanism physical model is obtained, and the exact and approximate solitary traveling wave solutions are found. As an example, it is pointed out that the solitary traveling wave approximate solutions have better accurate degree by using the homotopic mapping theory. (general)
Variable separation solutions and new solitary wave structures to the (1+1)-dimensional Ito system
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2006-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physics system.The variable separation solution of (1+1)-dimensional Ito system is obtained.Some special types of solutions such as non-propagating solitary wave solution,propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
Study of nonlinear ion- and electron-acoustic waves in multi-component space plasmas
G. S. Lakhina
2008-11-01
Full Text Available Large amplitude ion-acoustic and electron-acoustic waves in an unmagnetized multi-component plasma system consisting of cold background electrons and ions, a hot electron beam and a hot ion beam are studied using Sagdeev pseudo-potential technique. Three types of solitary waves, namely, slow ion-acoustic, ion-acoustic and electron-acoustic solitons are found provided the Mach numbers exceed the critical values. The slow ion-acoustic solitons have the smallest critical Mach numbers, whereas the electron-acoustic solitons have the largest critical Mach numbers. For the plasma parameters considered here, both type of ion-acoustic solitons have positive potential whereas the electron-acoustic solitons can have either positive or negative potential depending on the fractional number density of the cold electrons relative to that of the ions (or total electrons number density. For a fixed Mach number, increases in the beam speeds of either hot electrons or hot ions can lead to reduction in the amplitudes of the ion-and electron-acoustic solitons. However, the presence of hot electron and hot ion beams have no effect on the amplitudes of slow ion-acoustic modes. Possible application of this model to the electrostatic solitary waves (ESWs observed in the plasma sheet boundary layer is discussed.
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2004-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.
Oceanic pycnocline depth retrieval from SAR imagery in the existence of solitary internal waves
无
2005-01-01
Oceanic pycnocline depth is usually inferred from in situ measurements. It is attempted to estimate the depth remotely. As solitary internal waves occur on oceanic pycnocline and propagate along it, it is possible to retrieve the depth indirectly in virtue of the solitary internal waves. A numerical model is presented for retrieving the pycnocline depth from synthetic aperture radar (SAR) images where the solitary internal waves are visible and when ocean waters are fully stratified. This numerical model is constructed by combining the solitary internal wave model and a two-layer ocean model. It is also assumed that the observed groups of solitary internal wave packets on the SAR imagery are generated by local semidiurnal tides. A case study in the East China Sea shows a good agreement with in situ CTD (conductivity-temperature-depth) data.
Haider, M. M.; Rahman, O.
2016-07-01
An attempt has been made to study the multi-dimensional instability of dust-ion-acoustic (DIA) solitary waves (SWs) in magnetized multi-ion plasmas containing opposite polarity ions, opposite polarity dusts and non-thermal electrons. First of all, we have derived Zakharov-Kuznetsov (ZK) equation to study the DIA SWs in this case using reductive perturbation method as well as its solution. Small-k perturbation technique was employed to find out the instability criterion and growth rate of such a wave which can give a guideline in understanding the space and laboratory plasmas, situated in the D-region of the Earth's ionosphere, mesosphere, and solar photosphere, as well as the microelectronics plasma processing reactors.
Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements
Hossen, M. A., E-mail: armanplasma@gmail.com; Mamun, A. A., E-mail: mamun-phys@yahoo.co.uk [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-10-15
The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.
Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements
The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed
Identification and determination of solitary wave structures in nonlinear wave propagation
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
Features of fluid flows in strongly nonlinear internal solitary waves
S. Semin
2014-12-01
Full Text Available The characteristics of highly nonlinear solitary internal waves (solitons are calculated within the fully nonlinear numerical model of the Massachusetts Institute of Technology. The verification and adaptation of the model is based on the data from laboratory experiments. The present paper also compares the results of our calculations with the calculations performed in the framework of the fully nonlinear Bergen Ocean Model. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in the numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the pycnocline and near the bottom are computed.
FISSION LAWS OF INITIALLY INTERFACE SOLITARY WAVES IN TWO-LAYER OCEAN
XU Zhao-ting; SHEN Guo-jin; QIAO Fang-li
2004-01-01
A 2-D KdV equation of two-layer stratified ocean with 2-D topography is recapitulated in the present paper.Based on a reduced version of this 2-D KdV equation,the fission laws of the initially internal solitary waves are studied by means of numerical calculation.From the numerical results,it is shown that the initially interface solitary waves can fission on the continental slope like the initially surface solitary waves and the fission process is a significant generating mechanism of internal interface soliton packet on the continental shelf.
Propagation behavior of acoustic wave in wood
Huadong Xu; Guoqi Xu; Lihai Wang; Lei Yu
2014-01-01
We used acoustic tests on a quarter-sawn poplar timbers to study the effects of wood anisotropy and cavity defects on acoustic wave velocity and travel path, and we investigated acoustic wave propagation behavior in wood. The timber specimens were first tested in unmodified condition and then tested after introduction of cavity defects of varying sizes to quantify the transmitting time of acoustic waves in laboratory conditions. Two-dimensional acoustic wave contour maps on the radial section of specimens were then simulated and analyzed based on the experimental data. We tested the relationship between wood grain and acoustic wave velocity as waves passed in various directions through wood. Wood anisotropy has significant effects on both velocity and travel path of acoustic waves, and the velocity of waves passing longitudinally through timbers exceeded the radial velocity. Moreover, cavity defects altered acoustic wave time contours on radial sections of timbers. Acous-tic wave transits from an excitation point to the region behind a cavity in defective wood more slowly than in intact wood.
Sultana, S; Kourakis, I, E-mail: ssultana02@qub.ac.uk, E-mail: i.kourakis@qub.ac.uk [Centre for Plasma Physics, Department of Physics and Astronomy, Queen' s University Belfast, BT7 1NN Northern Ireland (United Kingdom)
2011-04-15
The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schroedinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different {kappa}) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.
Run-up of non-breaking double solitary waves with equal wave heights on a plane beach
王本龙; 董杰; 刘桦
2014-01-01
The evolution and run-up of double solitary waves on a plane beach were studied numerically using the nonlinear shallow water equations (NSWEs) and the Godunov scheme. The numerical model was validated through comparing the present numerical results with analytical solutions and laboratory measurements available for propagation and run-up of single solitary wave. Two successive solitary waves with equal wave heights and variable separation distance of two crests were used as the incoming wave on the open boundary at the toe of a slope beach. The run-ups of the first wave and the second wave with different separation distances were investigated. It is found that the run-up of the first wave does not change with the separation distance and the run-up of the second wave is affected slightly by the separation distance when the separation distance is gradually shortening. The ratio of the maximum run-up of the second wave to one of the first wave is related to the separation distance as well as wave height and slope. The run-ups of double solitary waves were compared with the linearly superposed results of two individual solitary-wave run-ups. The comparison reveals that linear superposition gives reasonable prediction when the separation distance is large, but it may overestimate the actual run-up when two waves are close.
Investigation of co-travelling solitary wave collisions in a granular chain
Anzel, Paul; Daraio, Chiara
2012-04-01
We present investigations into the collision of co-travelling solitary waves in a granular chain. Impulses are injected into the system by means of a piezo stack and the results are compared to a numerical model of discrete masses connected by non-linear springs. Similar to other solitary wave-carrying systems, a phase shift in both interacting solitary waves is observed due to their collision. Additionally, the formation of small secondary waves is observed in both numerical and experimental results. Insight into solitary wave interactions will be important for high-frequency excitation of a granular crystal, which may allow for improved Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM) methods.
Ion Acoustic Waves in the Presence of Electron Plasma Waves
Michelsen, Poul; Pécseli, Hans; Juul Rasmussen, Jens
1977-01-01
Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave.......Long-wavelength ion acoustic waves in the presence of propagating short-wavelength electron plasma waves are examined. The influence of the high frequency oscillations is to decrease the phase velocity and the damping distance of the ion wave....
Response of internal solitary waves to tropical storm Washi in the northwestern South China Sea
Z. H. Xu
2011-11-01
Full Text Available Based on in-situ time series data from an array of temperature sensors and an acoustic Doppler current profiler on the continental shelf of the northwestern South China Sea, a sequence of internal solitary waves (ISWs were observed during the passage of tropical storm Washi in the summer of 2005, which provided a unique opportunity to investigate the ISW response to the tropical cyclone. The passing tropical storm is found to play an important role in affecting the stratification structure of the water column, and consequently leading to significant variability in the propagating features of the ISWs, such as the polarity reversal and amplitude variations of the waves. The response of the ISWs to Washi can be divided into two stages, direct forcing by the strong wind (during the arrival of Washi and remote forcing via the near-inertial internal waves induced by the tropical storm (after the passage of Washi. The field observations as well as a theoretical analysis suggest that the variations of the ISWs closely coincide with the changing stratification structure and shear currents in accompanied by the typhoon wind and near-inertial waves. This study presents the first observations and analysis of the ISW response to the tropical cyclone in the South China Sea.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
Bypass transition of the bottom boundary layer under solitary wave
Sadek, Mahmoud; Diamessis, Peter; Parras, Luis; Liu, Philip
2015-11-01
The transition to turbulence in the bottom boundary layer (BBL) flow driven by a soliton-like pressure gradient in an oscillating water tunnel (an approximation for the BBL under solitary waves) is investigated using hydrodynamic linear stability theory and DNS. As observed in the laboratory experiment by Sumer et al. (2010), two possible transition scenarios exist. The first scenario is associated with the classical transition resulting from the breakdown of the exponentially growing 2-D Tollmien-Schlichting waves. The alternative scenario; i.e., bypass transition; takes place through formation of localized turbulent spots. The investigation of the latter transition scenario is performed in two steps. The first step consists of reformulating the linear stability analysis in the non-modal framework for the purpose of finding the optimum disturbance characteristics which lead to the formation of those turbulent spots. In the second step, the computed optimum noise structure is inserted in the 3D DNS in order to induce the formation of the turbulent spots and effectively simulate the bypass transition observed experimentally.
Obliquely propagating large amplitude solitary waves in charge neutral plasmas
F. Verheest
2007-01-01
Full Text Available This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not of the phase, since the amplitude or envelope graphs look very similar.
A Polynomial Expansion Method and New General Solitary Wave Solutions to KS Equation
PENG Yan-Ze
2003-01-01
Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.
Different Types of Solitary Wave Scattering in the Fermi-Pasta-Ulam Model
WEN Zhen-Ying; ZHAO Hong
2005-01-01
@@ We show that the scattering between two solitary waves in the Fermi-Pasta-Ulam model with interaction potential V(x) = αx2/2 + x4/4 can be classified into four types according to the configurations of the solitary waves. For three of the four types, the large solitary wave can lose energy and the small one can gain in average by collision.For the other one type in a special parameter region we encounter an anomalous scattering, i.e. the large solitary wave gains energy and the small one loses energy. Numerical investigations are performed for the anharmonic limit case of α = 0 and the general case of α≠ 0 and comparisons between them are made.
Weakly Two-Dimensional Solitary Waves on Coupled NonlinearTransmission Lines
段文山; 洪学仁; 石玉仁; 吕克璞; 孙建安
2002-01-01
We study the nonlinear solitary wave solution under the transverse perturbations for a system of coupled nonlinear electrical transmission lines. In the continuum limit and suitably scaled coordinates, the voltage on the system is described by a modified Zakharov-Kuznetsov equation. The cut-off frequency of the growth rate for the solitary waves under transverse perturbations has been analytically obtained. It is in agreement witl the cases p = 1/2 and p = I vhich have been studied previously.
The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation
Yuanxi Xie; Jilashi Tang
2006-03-01
In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.
Comparison of bed shear under non-breaking and breaking solitary waves
JayaKumar, S.; Baldock, T.E.
and bores of different amplitudes were generated. The typical wave paddle motion and resultant non-breaking solitary wave profiles generated is presented in Fig.2 whereas the paddle motion and resulting solitary bore profile is shown in Fig.3. For each... the forces generated on subsea infrastructure. Tsunamis are one such potential hazard 1 Research Higher Degree Candidate, School of Civil Engineering, The University of Queensland, Brisbane, QLD 4072...
Selim, M. M.; El-Depsy, A.; El-Shamy, E. F.
2015-12-01
Properties of nonlinear ion-acoustic travelling waves propagating in a three-dimensional multicomponent magnetoplasma system composed of positive ions, negative ions and superthermal electrons are considered. Using the reductive perturbation technique (RPT), the Zkharov-Kuznetsov (ZK) equation is derived. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave solutions and the periodic travelling wave solutions of the resulting ZK equation. It is found that both compressive and rarefactive nonlinear ion-acoustic travelling waves strongly depend on the external magnetic field, the unperturbed positive-to-negative ions density ratio, the direction cosine of the wave propagation vector with the Cartesian coordinates, as well as the superthermal electron parameter. The present model may be useful for describing the formation of nonlinear ion-acoustic travelling wave in certain astrophysical scenarios, such as the D and F-regions of the Earth's ionosphere.
On Collisionless Damping of Ion Acoustic Waves
Jensen, Vagn Orla; Petersen, P.I.
1973-01-01
Exact theoretical treatments show that the damping of ion acoustic waves in collisionless plasmas does not vanish when the derivative of the undisturbed distribution function at the phase velocity equals zero.......Exact theoretical treatments show that the damping of ion acoustic waves in collisionless plasmas does not vanish when the derivative of the undisturbed distribution function at the phase velocity equals zero....
Rogue wave variational modelling through the interaction of two solitary waves
Gidel, Floriane; Bokhove, Onno
2016-04-01
The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a
Characteristic behaviour of Kadomtsev-Petviashvili solitary waves and their stability in plasmas
By employing the reductive perturbation technique, Kadomtsev-Petviashvili (K-P) equation has been derived with a view to know the salient features of soliton propagation in multi-component plasma. A proposed method called as tanh-method has been employed to find the soliton solution of the non-linear K-P wave equation and has shown successfully the existence of various soliton propagation in plasma. The main aim of using the formalism of tanh-method has been given to modify the non-linear wave equation into an ordinary differential equation which has been solved ultimately by Frobenius method. In contrast to the earlier predictions, it has been shown that the multi-component plasma might not always sustain the compressive or rarefactive soliton even though the plasma consists of multi-temperature electrons. The existence depends on the control of plasma configuration which might be the advanced knowledge to observe the soliton formation in laboratory and space plasmas. Moreover, because of the higher order non-linearity, the observations sieved various plasma acoustic modes which could be of interest to relate in space plasmas. Finally, it has been shown that the solitary wave propagation though suffers from the bifurcation due to the singularity in the propagation, despite all, the study, based on the perturbation procedure, confirmed the stability of the soliton propagation irrespective of their different natures. (author)
Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments
Chitta, Subhashini; Steinhoff, John
2015-11-01
In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.
Linear Stability of the boundary layer under a solitary wave
Verschaeve, Joris C G
2013-01-01
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) reveal- ing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of stability for this otherwise unsteady flow. For the linear stability the Orr-Sommerfeld equation and the parabolic stability equation were used. The results are compared to key results of inviscid stability theory and validated by means of a direct numerical simulation using a Legendre-Galerkin spectral ele- ment Navier-Stokes solver. Special care has been taken to ensure that the numerical results are valid. Linear stability predicts that the boundary layer flow is unstable for the entire parameter range considered, conf...
Integrability: mathematical methods for studying solitary waves theory
Wazwaz, Abdul-Majid
2014-03-01
In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the
Solving solitary waves with discontinuity by means of the homotopy analysis method
An analytic method, namely the homotopy analysis method (HAM), is applied to solve solitary waves governed by Camassa-Holm equation. Purely analytic solutions are given for soliton waves with and without continuity at crest. This provides with a new analytic approach to solve soliton waves with discontinuity
Dust-acoustic solitary structures in plasmas with nonthermal electrons and positive dust
F. Verheest
2008-07-01
Full Text Available Large dust-acoustic solitons and kinks in dusty plasmas with positive cold dust, nonthermally distributed electrons and Boltzmann ions have been studied in a systematic way, to delimit their compositional parameter space. The existence domain of positive solitons is limited by infinite dust compression, of negative ones by the occurrence of potential kinks, provided the electrons are sufficiently nonthermal and there is sufficient positive charge on the dust. There is a parameter range where both negative and positive solitary structures coexist.
A Schamel equation for ion acoustic waves in superthermal plasmas
Williams, G., E-mail: gwilliams06@qub.ac.uk; Kourakis, I. [Centre for Plasma Physics, Department of Physics and Astronomy, Queen' s University Belfast, BT7 1NN, Northern Ireland (United Kingdom); Verheest, F. [Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B-9000 Gent (Belgium); School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000 (South Africa); Hellberg, M. A. [School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000 (South Africa); Anowar, M. G. M. [Department of Physics, Begum Rokeya University, Rangpur, Rangpur-5400 (Bangladesh)
2014-09-15
An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u{sub 0}. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.
Oba, Roger; Finette, Steven
2002-02-01
Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is
Exact solitary-wave, kink wave and singular solitary-wave solutions for Kadomtsev-Petviashvili (KP) equation with p-power (p > 1) of nonlinearity are obtained using a novel auxiliary equation and homogeneous balance method.
Unidirectional propagation of designer surface acoustic waves
Lu, Jiuyang; Ke, Manzhu; Liu, Zhengyou
2014-01-01
We propose an efficient design route to generate unidirectional propagation of the designer surface acoustic waves. The whole system consists of a periodically corrugated rigid plate combining with a pair of asymmetric narrow slits. The directionality of the structure-induced surface waves stems from the destructive interference between the evanescent waves emitted from the double slits. The theoretical prediction is validated well by simulations and experiments. Promising applications can be anticipated, such as in designing compact acoustic circuits.
Second-order dust acoustic wave theory
A second-order perturbation theory for non-dispersive, undamped dust acoustic waves is presented. The analysis leads to a second-order wave equation with source terms consisting of (nonlinear) products of first-order terms. The nonlinear effects included in this analysis might be useful in explaining the non-sinusoidal waveforms that are observed with large-amplitude, self-excited dust acoustic waves.
Singh, Satyavir; Bharuthram, Ramashwar
2016-07-01
Small amplitude electron acoustic solitary waves are studied in a magnetized plasma consisting of hot electrons following Cairn's type non-thermal distribution function and fluid cool electrons, cool ions and an electron beam. Using reductive perturbation technique, the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation is derived to describe the nonlinear evolution of electron acoustic waves. It is observed that the presence of non-thermal electrons plays an important role in determining the existence region of solitary wave structures. Theoretical results of this work is used to model the electrostatic solitary structures observed by Viking satellite. Detailed investigation of physical parameters such as non-thermality of hot electrons, beam electron velocity and temperature, obliquity on the existence regime of solitons will be discussed.
The propagation of a solitary wave over seabed mud of the Voigt model
Xia, YueZhang; Zhu, KeQin
2012-01-01
In shallow water, seabed mud can dissipate the energy of surface gravity waves effectively. In this paper, solitary wave attenuation induced by seabed mud is studied based on a two-layered system, in which the water is assumed to be inviscid and the mud layer is described by the Voigt model. A set of Boussinesq-type equations suitable for solitary waves over the mud of the Voigt model is established, by combining the perturbation analysis and the Laplace transformation. Degenerating into the case of Newtonian model, our Boussinesq-type equations are equivalent to those of Liu and Chan (2007), while the term indicating mud influence is greatly simplified. Based on the equations, the attenuation of solitary waves is studied. An evolution equation of wave amplitude is obtained and the development of mud velocity profiles is discussed. The modal analysis shows that the first mode always dominates mud dynamics. The results are also compared with those of the Maxwell model.
Saha, Asit; Pal, Nikhil; Saha, Tapash; Ghorui, M. K.; Chatterjee, Prasanta
2016-06-01
Bifurcations and chaotic behaviors of dust acoustic traveling waves in magnetoplasmas with nonthermal ions featuring Cairns-Tsallis distribution is investigated on the framework of the further modified Kadomtsev-Petviashili (FMKP) equation. The FMKP equation is derived employing the reductive perturbation technique (RPT). Bifurcations of dust acoustic traveling waves of the FMKP equation is presented. Using the bifurcation theory of planar dynamical systems, two new analytical traveling wave solutions for solitary and periodic waves are derived depending on the parameters α , α _1, q, l and U. Considering an external periodic perturbation, the chaotic behavior of dust acoustic traveling waves is investigated through quasiperiodic route to chaos. The parameter q significantly affects the chaotic behavior of the perturbed FMKP equation.
CHEN Yong; YAN Zhen-Ya; LI Biao; ZHANG Hong-Qing
2002-01-01
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
Head-on collision of large amplitude internal solitary waves of the first mode
Terletska, Kateryna; Maderich, Vladimir; Brovchenko, Igor; Jung, Kyung Tae; Talipova, Tatiana
2016-04-01
The dynamics and energetics of a frontal collision of internal solitary waves of depression and elevation of moderate and large amplitudes propagating in a two-layer stratified fluid are studied numerically in frame of the Navier-Stokes equations. It was considered symmetric and asymmetric head-on collisions. We propose the dimensionless characteristic of the wave collision ξ that is the ratio of the wave steepnesses. Wave runup normalized on the amplitude of incoming wave as function of the waves steepness is proposed. Interval 01 corresponds to the larger wave in the case of asymmetric collision. Results of modeling were compared with the results of laboratory experiments [1]. It was shown that the frontal collision of internal solitary waves of moderate amplitude leads to a small phase shift and to the generation of dispersive wavetrain trailing behind transmitted solitary wave. The phase shift grows with increasing amplitudes of the interacting waves and approaches the limiting value when amplitudes of the waves are equal to the upper/lower layer for waves of depression/elevation. The deviation of the maximum wave height during collision from the twice the amplitude are maximal when wave amplitudes are equal to the upper/lower layer for waves of depression/elevation, then it decays with growth of amplitudes of interacting waves. It was found that the interaction of waves of large amplitude leads to the shear instability and the formation of Kelvin - Helmholtz vortices in the interface layer, however, subsequently waves again become stable. References [1] R.-C. Hsu, M. H. Cheng, C.-Y. Chen, Potential hazards and dynamical analysis of interfacial solitary wave interactions. Nat Hazards. 65 (2013) 255-278
The Korteweg-de Vries-Zakharov-Kuznetsov equation for electron-acoustic waves
Motivated by a recent paper [Phys. Plasmas 7, 2987 (2000)] highlighting the potential importance of the electron-acoustic wave in interpreting the solitary waves observed by high time resolution measurements of the electric field in the auroral region, the effect of a magnetic field on weakly nonlinear electron-acoustic waves is investigated. A Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation is derived for a plasma comprised of cool and hot electrons and a species of fluid ions. Two models are employed for the ions: magnetized and unmagnetized. When the ions are magnetized the frequency constraints imposed upon the electron-acoustic wave packet prove to be too limiting to be of general use. The second model, which treats the ions as a stationary neutralizing background, overcomes the restrictions imposed by the former and is more fitting for the frequency domain of the electron-acoustic wave. Plane and ellipsoidal soliton solutions are admitted by the KdV-ZK equation, the latter perhaps able to explain some of the two dimensional features of the solitary waves observed in the Earth's high altitude auroral region. Both models for the ions predict only negative potential solitons. It is discussed how the plasma model might be adapted to produce positive potential solitons
RANS-VOF solver for solitary wave run-up on a circular cylinder
Cao, Hong-jian; Wan, De-cheng
2015-04-01
Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes OpenFOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier-Stokes (RANS) equations with the SST k- ω turbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid (VOF) technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.
RANS-VOF Solver for Solitary Wave Run-up on A Circular Cylinder
曹洪建; 万德成
2015-01-01
Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes OpenFOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier–Stokes (RANS) equations with the SST k-wturbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid (VOF) technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.
Algebraic Rossby Solitary Waves Excited by Non-Stationary External Source
杨红卫; 尹宝树; 董焕河; 时云龙
2012-01-01
The paper deals with the effects of non-stationary external source forcing and dissipation on algebraic Rossby solitary waves. From quasi-geostrophic potential vorticity equation, basing on the multiple-scale method, an inhomogeneous Korteweg-de Vries-Benjamin Ono Burgers （KdV-B-O-Burgers） equation is obtained. This equation has not been previously derived for Rossby waves. By analysis and calculation, four conservation laws associated with the above equation are first obtained. With the help of pseudo-spectral method, the waterfall plots are obtained and the evolutional characters of algebraic Rossby solitary waves are studied. The results show that non-stationary external source and dissipation have great effect on the generation and evolution of algebraic solitary Rossby waves.
Numerical simulations of the local generation of internal solitary waves in the Bay of Biscay
N. Grisouard
2010-10-01
Full Text Available Oceanic observations from the Bay of Biscay, Portugal, Mozambique Channel and Mascarene Ridge have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the thermocline from below – a process referred to as "local generation". Here we present two-dimensional numerical simulations with a fully nonlinear nonhydrostatic model of situations that are relevant for the Bay of Biscay in summer. We show that a beam impinging on a thermocline initially at rest can induce a displacement of the isopycnals, large enough for internal solitary waves to be generated. These internal solitary waves however differ from those observed in the Bay of Biscay through their amplitude and distance between wave trains. We then show that the latter feature is recovered when the background flow around the thermocline as found in the Bay of Biscay is included in the forcing, thereby yielding a more accurate view on the local generation mechanism.
Analysis of solitary wave impulses in granular chains using ultrasonic excitation
Yang, J.; Hutchins, D. A.; Akanji, O.; Thomas, P. J.; Davis, L. A. J.; Harput, S.; Gelat, P.; Freear, S.; Saffari, N.
2016-06-01
The propagation of broad bandwidth solitary wave impulses, generated within granular chains by narrow bandwidth ultrasonic excitation, is studied in detail. Theoretical predictions are compared to experimental results. It is demonstrated that the observed effects result from a sum of a solitary wave traveling out from the source with a wave that reflects from the far end of the chain. It is shown that this combination, when used with an excitation in the form of a long-duration tone burst, encourages the generation of multiple impulses with a characteristic periodicity. This study shows that the properties of the chain structure and the excitation can be adjusted so as to generate ultrasonic solitary wave impulses with a high amplitude and known frequency content, which are of interest in applications such as biomedical ultrasound.
Numerical simulations of the local generation of internal solitary waves in the Bay of Biscay
Grisouard, N.; Staquet, C.
2010-10-01
Oceanic observations from the Bay of Biscay, Portugal, Mozambique Channel and Mascarene Ridge have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the thermocline from below - a process referred to as "local generation". Here we present two-dimensional numerical simulations with a fully nonlinear nonhydrostatic model of situations that are relevant for the Bay of Biscay in summer. We show that a beam impinging on a thermocline initially at rest can induce a displacement of the isopycnals, large enough for internal solitary waves to be generated. These internal solitary waves however differ from those observed in the Bay of Biscay through their amplitude and distance between wave trains. We then show that the latter feature is recovered when the background flow around the thermocline as found in the Bay of Biscay is included in the forcing, thereby yielding a more accurate view on the local generation mechanism.
Beyer, Robert
1981-01-01
Surveys 50 years of acoustical studies by discussing selected topics including the ear, nonlinear representations, underwater sound, acoustical diagnostics, absorption, electrolytes, phonons, magnetic interaction, and superfluidity and the five sounds. (JN)
Linear stability of multiple internal solitary waves in fluids of great depth
Matsuno, Y.; Kaup, D. J.
1997-02-01
The linear stability of the multiple solitary wave solution of the Benjamin-Ono (BO) equation is studied analytically. By establishing the completeness relation for the eigenfunctions of the BO equation linearized about multisoliton solutions, we solve the initial value problem for this system. We find that the wave under consideration is stable against infinitesimal perturbations.