共查询到20条相似文献,搜索用时 31 毫秒
1.
Taking the (2+1)-dimensional
Broer-Kaup-Kupershmidt system as a simple example, some families
of rational form solitary wave solutions, triangular periodic
wave solutions, and rational wave solutions are constructed by
using the Riccati equation rational expansion method presented
by us. The method can also be applied to solve more nonlinear
partial differential equation or equations. 相似文献
2.
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations.
With the aid of symbolic computation, we apply the proposed method
to solving the (1+1)-dimensional dispersive long wave equation and
explicitly construct a series of exact solutions which include the
rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases. 相似文献
3.
By means of two different Riccati
equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1)-dimensional dispersive long wave equation are successfully constructed, which include various combination of
trigonometric periodic and hyperbolic function solutions, various
combination of trigonometric periodic and rational function
solutions, and various combination of hyperbolic and rational
function solutions. 相似文献
4.
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation. 相似文献
5.
The(3+1)-dimensional Zakharov–Kuznetsov(ZK) and the new extended quantum ZK equations are functional to decipher the dense quantum plasma, ion-acoustic waves, electron thermal energy,ion plasma, quantum acoustic waves, and quantum Langmuir waves. The enhanced modified simple equation(EMSE) method is a substantial approach to determine competent solutions and in this article, we have constructed standard, illustrative, rich structured and further comprehensive soliton solutions via this method. The solutions are ascertained as the integration of exponential, hyperbolic,trigonometric and rational functions and formulate the bright solitons, periodic, compacton, bellshape, parabolic shape, singular periodic, plane shape and some new type of solitons. It is worth noting that the wave profile varies as the physical and subsidiary parameters change. The standard and advanced soliton solutions may be useful to assist in describing the physical phenomena previously mentioned. To open out the inward structure of the tangible incidents, we have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the EMSE technique for extracting soliton solutions to nonlinear evolution equations is efficient, compatible and reliable in nonlinear science and engineering. 相似文献
6.
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions. 相似文献
7.
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 相似文献
8.
Based on the extended mapping deformation method and symbolic
computation, many exact travelling wave solutions are found for
the (3+1)-dimensional JM equation and the (3+1)-dimensional KP
equation. The obtained solutions include solitary solution, periodic wave solution,
rational travelling wave solution, and Jacobian and Weierstrass
function solution, etc. 相似文献
9.
ZHENG Chun-Long FEI Jin-Xi 《理论物理通讯》2007,48(4):657-661
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solltary wave solutlons, periodic wave solutions and rational function solutions) with arbitrary functions [or the (2+ 1)-dimensional general/zed Broer-Kaup (GBK) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the (2+1)-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed. 相似文献
10.
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic
form solutions, are obtained. 相似文献
11.
A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System 总被引:1,自引:0,他引:1
BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2007,48(5):801-810
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation. 相似文献
12.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixtb-aegree nonnneal term, we study the (2+l )-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations. 相似文献
13.
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixth-degree nonlinear term, we study the (2 1)-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations. 相似文献
14.
15.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(11)
The singular manifold method is used to obtain two general solutions to a (2 1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
16.
In this pager a pure algebraic method implemented in a computer
algebraic system, named multiple Riccati equations rational
expansion method, is presented to construct a novel class of
complexiton solutions to integrable equations and nonintegrable
equations. By solving the (2+1)-dimensional dispersive long wave
equation, it obtains many new types of complexiton solutions such as
various combination of trigonometric periodic and hyperbolic
function solutions, various combination of trigonometric periodic
and rational function solutions, various combination of hyperbolic
and rational function solutions, etc. 相似文献
17.
An extended subequation rational expansion method is presented and
used to construct some exact analytical solutions of the (2+1)-dimensional
cubic nonlinear Schrödinger equation. From our results, many known
solutions of the (2+1)-dimensional cubic nonlinear Schrödinger
equation can be recovered by means of some suitable selections of
the arbitrary functions and arbitrary constants. With computer simulation,
the properties of new non-travelling wave and coefficient function's
soliton-like solutions, and elliptic solutions are demonstrated by some plots. 相似文献
18.
BIAN Xue-Jun 《理论物理通讯》2005,44(11)
An algebraic method is proposed to solve a new (2 1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions. 相似文献
19.
With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional generalized Breor-Kaup (GBK) system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons. 相似文献
20.
BIAN Xue-Jun 《理论物理通讯》2005,44(5):815-820
An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions. 相似文献