共查询到20条相似文献,搜索用时 15 毫秒
1.
A Wronskian form expansion method is proposed to construct novel composite function solutions to the modified Korteweg-de Vries (mKdV) equation. The method takes advantage of the forms and structures of Wronskian solutions to the mKdV equation, and Wronskian entries do not satisfy linear partial differential equations. The method can be automatically carried out in computer algebra (for example, Maple). 相似文献
2.
2+1 维变系数广义KP方程的椭圆周期解 总被引:1,自引:0,他引:1
田贵辰 《高校应用数学学报(A辑)》2005,20(2):239-243
运用Jacobi椭圆函数展开法求得了2 1维变系数广义KadoratsevPetviashvili方程的椭圆周期解及孤立波解. 相似文献
3.
Baojian Hong 《Applied mathematics and computation》2010,217(2):472-479
In this paper, an generalized Jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact Jacobi elliptic functions solutions of the generalized coupled Hirota-Satsuma KdV system. As a result, eight families of new doubly periodic solutions are obtained by using this method, some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the Jacobi elliptic functions m → 1 or 0, which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics. 相似文献
4.
This paper is concerned with several aspects of travelling wave solutions for a (N+1) dimensional potential KdV equation. The Weierstrass elliptic function solutions, the Jaccobi elliptic function solutions, solitary wave solutions, periodic wave solutions to the equation are acquired under certain circumstances. It is shown that the coefficients of derivative terms in the equation cause the qualitative changes of physical structures of the solutions. 相似文献
5.
New exact solutions for a generalized variable-coefficient KdV equation were obtained using the generalized expansion method [R. Sabry, M.A. Zahran, E.G. Fan, Phys. Lett. A 326 (2004) 93]. The obtained solutions include solitary wave solutions besides Jacobi and Weierstrass doubly periodic wave solutions. 相似文献
6.
Erik Sweet 《Applied mathematics and computation》2010,216(10):2783-4166
Analytical solutions to the generalized Drinfel’d-Sokolov (GDS) equations
7.
一般变系数KdV方程的精确解 总被引:7,自引:0,他引:7
LiuXiqiang JiangSong 《高校应用数学学报(英文版)》2001,16(4):377-380
By asing the nonclassical method of symmetry reductions, the exact solutions for general variable-coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don‘t exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable-coefficient KdV equation is given. 相似文献
8.
广义组合KdV-mKdV方程的显式精确解 总被引:1,自引:0,他引:1
Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations. 相似文献
9.
Numerical solution of the Korteweg-de Vries equation is obtained by using the meshless method based on the collocation with radial basis functions. Five standard radial basis functions are used in the method of the collocation. The results are compared for the numerical experiments of the propagation of solitons, interaction of two solitary waves and breakdown of initial conditions into a train of solitons. 相似文献
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11.
In this paper, the nonlocal symmetries and exact interaction solutions of the variable coefficient Korteweg–de Vries (KdV) equation are studied. With the help of pseudo-potential, we construct the high order nonlocal symmetries of the time-dependent coefficient KdV equation for the first time. In order to construct the new exact interaction solutions, two auxiliary variables are introduced, which can transform nonlocal symmetries into Lie point symmetries. Furthermore, using the Lie point symmetries of the closed system, some exact interaction solutions are obtained. For some interesting solutions, such as the soliton–cnoidal wave solutions are discussed in detail, and the corresponding 2D and 3D figures are given to illustrate their dynamic behavior. 相似文献
12.
In this paper, a series of abundant exact travelling wave solutions is established for a modified generalized Vakhnenko equation by using auxiliary equation method. These solutions can be expressed by Jacobi elliptic function. When Jacobi elliptic functions modulus m→1 or 0, the travelling wave solutions degenerate to four types of solutions, namely, the soliton solutions, the hyperbolic function solutions, the trigonometric function solutions, constant solutions. 相似文献
13.
NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION 总被引:1,自引:0,他引:1
LetΩbe a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -△pu=|u|q-1u λf(x) onΩ, and identify necessary and sufficient conditions onΩand f(x) which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration. 相似文献
14.
HONG BAO-JIAN 《东北数学》2012,28(1)
In this paper,a new generalized Jacobi elliptic function expansion method based upon four new Jacobi elliptic functions is described and abundant solutions of new Jacobi elliptic functions for the gene... 相似文献
15.
In this paper, by using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by Mathematical software. 相似文献
16.
引入改进的F-广义方法,并将其应用于(2+1)维Nizhnik-Novikov-Veselov(NNV)方程.在符号计算软件的帮助下,可以得到NNV方程的许多新解.该方法用于获取包括雅可比椭圆函数解的一系列解,在数学物理中可应用于其他的非线性偏微分方程. 相似文献
17.
The variational iteration method (VIM) is applied to solve numerically the improved Korteweg-de Vries equation (IKdV). A correction function is constructed with a general Lagrange multiplier that can be identified optimally via the variational theory. This technique provides a sequence of functions with easily computable components that converge rapidly to the exact solution of the IKdV equation. Propagation of single, interaction of two, and three solitary waves, and also birth of solitons have been discussed. Three invariants of motion have been evaluated to determine the conservation properties of the problem. This procedure is promising for solving other nonlinear equations. 相似文献
18.
《Mathematical Methods in the Applied Sciences》2018,41(9):3316-3322
The Heisenberg ferromagnetic spin chain equation is investigated. By applying the improved F‐expansion method (Exp‐function method) and the Jacobi elliptic method, respectively, a series of exact solutions is constructed. The parametric conditions of the existence for the solutions are presented. These solutions comprise periodic wave solutions, doubly periodic wave solutions, and dark and bright soliton solutions, which are expressed in several different function forms, namely, Jacobi elliptic function, trigonometric function, hyperbolic function, and exponential function. The results illustrate that the Exp‐function method is a powerful symbolic algorithm to look for new solutions for the nonlinear evolution systems. 相似文献
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20.
Baojian Hong 《Applied mathematics and computation》2009,215(8):2908-2913
In this work, a new generalized Jacobi elliptic functions expansion method based upon four new Jacobi elliptic functions is described and abundant new Jacobi-like elliptic functions solutions for the variable-coefficient mKdV equation are obtained by using this method, some of these solutions are degenerated to solitary-like solutions and triangular-like functions solutions in the limit cases when the modulus of the Jacobi elliptic functions m→1 or 0, which shows that the new method can be also used to solve other nonlinear partial differential equations in mathematical physics. 相似文献