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Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new. 相似文献
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《Physics letters. A》2020,384(9):126201
In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schrödinger type equations through bilinearization procedure. In particular, we consider coupled nonlinear Schrödinger (CNLS) equations (both focusing as well as mixed type nonlinearities), coherently coupled nonlinear Schrödinger (CCNLS) equations and long-wave-short-wave resonance interaction (LSRI) system. We point out that the obtained general form of soliton solutions exhibit novel profile structures than the previously known degenerate soliton solutions corresponding to identical wave numbers in both the modes. We show that such degenerate soliton solutions can be recovered from the newly derived nondegenerate soliton solutions as limiting cases. 相似文献
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M S Osman K U Tariq Ahmet Bekir A Elmoasry Nasser S Elazab M Younis Mahmoud Abdel-Aty 《理论物理通讯》2020,72(3):35002-13
The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena. 相似文献
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In this paper, we improve some key steps in the homogeneous balance method (HBM), and propose a modified homogeneous balance
method (MHBM) for constructing multiple soliton solutions of the nonlinear partial differential equation (PDE) in a unified
way. The method is very direct and primary; furthermore, many steps of this method can be performed by computer. Some illustrative
equations are investigated by this method and multiple soliton solutions are found. 相似文献
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Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation 下载免费PDF全文
Xuefeng Zhang 《中国物理 B》2023,32(1):10505-010505
We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics. 相似文献
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This paper develops the Hirota method carefully for applying into the growing model of quasi-one-dimensional Bose—Einstein condensations with attractive and repulsive interaction, respectively. After a tedious calculation it obtains the exact bright and dark soliton solutions analytically.
It shows that the growing model has the important effect on the soliton amplitude and the time-dependent potential only contributes to the phase and phase velocity. A detailed analysis for the asymptotic behaviour of two-soliton solutions shows that the collision of two soliton is elastic. 相似文献
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In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance. 相似文献
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Starting from local coupled Hirota equations,we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem.The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair.By Lax pair,an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found.The solutions with specific properties are distinct from those of the local Hirota equation.In order to further describe the properties and the dynamic features of the solutions explicitly,several kinds of graphs are depicted. 相似文献
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Abdul-Majid Wazwaz 《Waves in Random and Complex Media》2020,30(4):776-786
ABSTRACT In this work, we develop two new integrable Kadomtsev–Petviashvili (KP) equations with time-dependent coefficients. The integrability property of each equation is explicitly demonstrated exhibiting the Painlevé test to confirm its integrability. Moreover, each equation admits multiple real and multiple complex soliton solutions. We introduce complex forms of the simplified Hirota's method to derive multiple complex soliton solutions. These two model equations are likely to be of applicative relevance, because it may be considered an application of a large class of nonlinear KP equations. 相似文献
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With the aid of the symbolic computation, we improve Xie's algorithm [F. Xie, Z.Y. Yan, H. Zhang, Phys. Lett. A 285 (2001) 76], and present a new extended method. Based on the new general ansatz (3), we successfully solve a compound KdV-MKdV equation, and obtain some special solutions which contain soliton solutions, and periodic solutions. The method can also be applied to other nonlinear partial differential equations. 相似文献
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The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique. 相似文献
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采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
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采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解.
关键词:
(3+1)维Nizhnik-Novikov-Veselov方程
非线性Klein-Gordon方程
孤子解
周期解 相似文献
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