共查询到20条相似文献,搜索用时 140 毫秒
1.
Based on the modified Sawada-Kotera equation, we introduce a 3 × 3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawada-Kotera equation, by which a Lax pair of the modified Sawada-Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawada-Kotera equation, the Kaup-Kupershmidt equation, and the modified Sawada-Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada-Kotera equation are constructed with the aid of their Lax pairs. 相似文献
2.
The soliton-like solutions to the (2+1)-dimensional modified dispersive water-wave system 总被引:1,自引:0,他引:1 下载免费PDF全文
By a simple transformation, we reduce the (2 1)-dimensional modified dispersive water-wave system to a simple nonlinear partial differential equation. In order to solve this equation by generalized tanh-function method, we only need to solve a simple system of first-order ordinary differential equations, and by doing so we can obtain many new soliton-like solutions which include the solutions obtained by using the conventional tanh-function method. 相似文献
3.
Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili (vKP) equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation. 相似文献
4.
A New Method for Constructing Travelling Wave Solutions to the modified Benjamin--Bona--Mahoney Equation 下载免费PDF全文
We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified BenjaminBona-Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions, It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. 相似文献
5.
Solutions of Two Kinds of Non-Isospectral Generalized Nonlinear Schrodinger Equation Related to Bose-Einstein Condensates 下载免费PDF全文
Two non-isospectral generalized nonlinear Schrodinger (ONLS) equations, which are two important models of nonlinear excitations of matter waves in Bose-Einstein condensates, are studied. Two novel transformations are constructed such that these two GNLS equations are transformed to the well-known nonlinear Schr6dinger (NLS) equation, which is an isospectral equation. Therefore, once one solution of the NLS equation is provided, we can immediately obtain one solution for two ONLS equations by these transformations. Thus it is unnecessary to solve these two non-isospectral GNLS equations directly. Soliton solutions and periodic solutions are obtained for them by two transformations from the corresponding solutions of the NLS equation, which are generated by Darboux transformation. 相似文献
6.
YANG Xian-Lin TANG Jia-Shi 《理论物理通讯》2008,50(11):1047-1051
The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
7.
<正>To seek new infinite sequence of exact solutions to nonlinear evolution equations,this paper gives the formula of nonlinear superposition of the solutions and Backlund transformation of Riccati equation.Based on the tanhfunction expansion method and homogenous balance method,new infinite sequence of exact solutions to Zakharov-Kuznetsov equation,Karamoto-Sivashinsky equation and the set of(2+l)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica.The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations. 相似文献
8.
Since the Jost solutions of the derivative nonlinear Schrodinger equation do not tend to the free Jost solutions, when the spectral parameter tends to infinity(|A|→∞), the usual inverse scattering transform (IST) must be revised. If we take the parameter κ = λ^-1 as the basic parameter, the Jost solutions in the limit of |κ|→∞ do tend to the free Jost solutions, hence the usual procedure to construct the equations of IST in κ-plane remains effective. After we derive the equation of IST in terms of κ, we can obtain the equation of IST in λ-plane by the simple change of parameters λ = κ^-1. The procedure to derive the equation of IST is reasonable, and attention is never paid to the function W(x) introduced by the revisions of Kaup and Newell. Therefore, the revision of Kaup and Newell can be avoided. 相似文献
9.
In this article, we propose an alternative approach of the generalized and improved (G'/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations. 相似文献
10.
《中国科学:物理学 力学 天文学(英文版)》2010,(8)
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives. 相似文献
11.
Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2 1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach. 相似文献
12.
13.
A nonlinear transformation and some
multi-solition solutions for the (2+1)-dimensional generalized
Broer-Kaup (GBK) system is first given by using the homogeneous
balance method. Then starting from the nonlinear transformation,
we reduce the (2+1)-dimensional GBK system to a simple linear
evolution equation. Solving this equation, we can obtain some new
explicit exact solutions of the original equations
by means of the extended hyperbola function method. 相似文献
14.
15.
An extended functional transformation method and its application in some evolution equations 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact,is a solution of the famous KdV equation, so this transformation
gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation. 相似文献
16.
An explicit N-fold Darboux transformation for evolution equations determined by general 2×2 AKNS system is constructed. By using the Darboux transformation, the solutions of the evolution equations are reduced to solving alinear algebraic system, from which a unified and explicit formulation of 2N-soliton solutions for the evolution equation are given. Furthermore, a reduction technique for MKdV equation is presented, and an N-fold Darboux transformation of MKdV hierarchy is constructed through the reduction technique. A Maple package which can entirely automatically output the exact N-soliton solutions of the MKdV equation is developed. 相似文献
17.
An integrable Gross–Pitaevskii equation with a parabolic potential is presented where particle density ∣u∣2 is conserved. We also present an integrable vector Gross–Pitaevskii system with a parabolic potential, where the total particle density ${\sum }_{j=1}^{n}| {u}_{j}{| }^{2}$ is conserved. These equations are related to nonisospectral scalar and vector nonlinear Schrödinger equations. Infinitely many conservation laws are obtained. Gauge transformations between the standard isospectral nonlinear Schrödinger equations and the conserved Gross–Pitaevskii equations, both scalar and vector cases are derived. Solutions and dynamics are analyzed and illustrated. Some solutions exhibit features of localized-like waves. 相似文献
18.
Bilinear Bcklund transformation and explicit solutions for a nonlinear evolution equation 下载免费PDF全文
The bilinear form of two nonlinear evolution equations are
derived by using Hirota derivative. The B\"{a}cklund transformation
based on the Hirota bilinear method for these two equations are
presented, respectively. As an application, the explicit solutions
including soliton and stationary rational solutions for these two
equations are obtained. 相似文献
19.
HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(3):325-328
By using the extended homogeneous balance method, a new auto-Ba^ecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively. 相似文献