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HUANG Wen-Hua ZHANG Jie-Fang 《理论物理通讯》2004,42(7)
Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton. 相似文献
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HUANG Ling 《理论物理通讯》2006,45(5):781-784
The exact solutions of a new coupled Burgers system are studied in
three different ways. The first type of solutions are found thanks
to the coupled Burgers system possessing a simple single Burgers
reduction. The second type of multiple soliton solutions are
revealed via the decouple procedure. The third type of exact
solutions are found by means of a prior ansatz and solutions of
the heat conduction equation. Two different kinds of soliton
fission phenomena of the model are discovered and a special type of
completely elastic soliton collision without phase shift of
the model is also displayed. 相似文献
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In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained. 相似文献
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HUANGWen-Hua ZHANGJie-Fang 《理论物理通讯》2004,42(1):4-8
Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton. 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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This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed. 相似文献
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WU Hong-Xia ZENG Yun-Bo FAN Tian-You 《理论物理通讯》2008,49(3):529-534
Darboux transformation (DT) provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV (eKdV) equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 (1999) 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail. 相似文献
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BAI Cheng-Jie HAN Ji-Guang WANG Wei-Tao AN Hong-Yong 《理论物理通讯》2008,49(5):1241-1244
The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort. 相似文献
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《Waves in Random and Complex Media》2013,23(4):439-451
In this paper, we acquire the soliton solutions of the nonlinear Schrodinger’s equation with dual power-law nonlinearity. Primarily, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some exact solutions including soliton solutions, rational and elliptic function solutions of this equation using the extended trial equation method. 相似文献
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To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations. 相似文献
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《Waves in Random and Complex Media》2013,23(3):417-428
In this work, we survey exact solutions of Sasa–Satsuma equation (SSE). We utilize extended trial equation method (ETEM) and generalized Kudryashov method to acquire exact solutions of SSE. First of all, we gain some exact solutions such as soliton solutions, rational, Jacobi elliptic, and hyperbolic function solutions of SSE by means of ETEM. Furthermore, we procure dark soliton solution of this equation by the help of generalized Kudryashov method. Lastly, for certain parameter values, we draw two- and three-dimensional graphics of imaginary and real values of some exact solutions that we achieved using these methods. 相似文献
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利用双线性方法给出了2+1维Sawaka-Kotera(SK)方程的N孤子解.将N孤子解中的实参数扩大到复数范围,得到了该方程的呼吸子解,描述线孤子和y周期孤子相互作用的解和两个y周期孤子相互作用的解.从解析和几何两个角度探讨了两个y周期孤子的相互作用.相互作用性质和耦合系数有关.对于SK方程,耦合系数的取值只允许方程中存在弹性的排斥相互作用.
关键词:
y周期孤子相互作用
SK方程
双线性方法 相似文献
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HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(2):171-174
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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Wei-Ping Zhong Milivoj Belić 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2014,68(11):1-6
An exact (2 + 1)-dimensional spatial optical soliton of the nonlinear Schrödinger equation with a spatially modulated nonlinearity and a special external potential is discovered in an inhomogeneous nonlinear medium, by utilizing the similarity transformation. Exact analytical solutions are constructed by the products of Whittaker functions and the bright and dark soliton solutions of the standard stationary nonlinear Schrödinger equation. Some examples of such composed solutions are given, in which these spatial solitons display different localized structures. Numerical calculation shows that the soliton is stable in propagating over long distances, thus also confirming the validity of the exact solution. 相似文献
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High-energy optical Schrödinger solitons 总被引:1,自引:0,他引:1
The conditions for the existence of a Lax pair were determined and exact analytic solutions to the nonlinear evolution equations of the Schrödinger type with complex and nonuniform potentials were found. In particular, these solutions provide a basis for the soliton management concept in applied problems and solve the problems of optimal energy accumulation by a Schrödinger soliton in an active medium and soliton amplification in optical fiber communication lines and soliton lasers. 相似文献
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In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions. 相似文献