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1.
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u, ux)uxx +B(u, ux) is studied by using the conditional Lie–Ba¨cklund symmetry method. The variant forms of the considered equations,which admit the corresponding conditional Lie–Ba¨cklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. 相似文献
2.
Variable Separation and Exact Solutions to Generalized Nonlinear Diffusion Equations 总被引:3,自引:0,他引:3 下载免费PDF全文
《中国物理快报》2002,19(12):1741-1744
We study in detail a method to find the generalized nonlinear diffusion equations,which can be solved by means of the variable separation approach.A complete list of canonical forms for such equations,which admit the functional separable solutions,is botained and some exact solutions to the resulting equations are described. A number of methods have been proven to be effective for finding symmetry reductions and constructing exact solutions to nonlinear diffusion equations. 相似文献
3.
Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave-short-wave resonant interaction 下载免费PDF全文
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately. 相似文献
4.
ZHANG Shun-Li LOU Sen-Yue 《理论物理通讯》2007,48(3):385-390
This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions (FSSs) and construct some exact FSSs to the resulting equations. 相似文献
5.
Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method 总被引:1,自引:0,他引:1
We consider the functional separation of variables to the nonlinear diffusion equation with source and convection termut = (A(x)D(u)ux)x B(x)Q(u),Ax ≠ 0.The functional separation of variables to this equation is studied by using the group foliation method.A classification is carried out for the equations which admit the function separable solutions.As a consequence,some solutions to the resulting equations are obtained. 相似文献
6.
New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients 下载免费PDF全文
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients. 相似文献
7.
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt=Au,uxuxx+Bu,ux,ut which admits the derivative-dependent functional separable solutions DDFSSs). We also extend the concept of the DDFSS to cover other variable separation approaches. 相似文献
8.
Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source 下载免费PDF全文
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = (A(u)Ux)x + eB(u, Ux). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples. 相似文献
9.
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
10.
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic
potential vorticity equation 下载免费PDF全文
By means of the reductive perturbation method, three types
of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP)
equations are derived from the baroclinic potential vorticity (BPV)
equation, including the modified KP (mKP) equation, standard KP equation
and cylindrical KP (cKP) equation. Then some solutions of
generalized cKP and KP equations with certain conditions are given
directly and a relationship between the generalized mKP equation and
the mKP equation is established by the symmetry group direct method
proposed by Lou et al. From the relationship and the solutions
of the mKP equation, some solutions of the generalized mKP equation can be
obtained. Furthermore, some approximate solutions of the baroclinic
potential vorticity equation are derived from three types of
generalized KP equations. 相似文献
11.
Considering that there are abundant coherent solitent soliton excitations in high dimensions,we reveal a novel phenomenon that the localized excitations possess chaotic and fractal behaviour in some(2 1)-dimensional soliton systems.To clarify the interesting phenomenon,we take the generalized(2 1)-dimensional Nizhnik-Novikov-Vesselov system as a concrete example,A quite general variable separation solutions of this system is derived via a variable separation approach first.then some new excitations like chaos and fractals are derived by introducing some types of lower-dimensional chaotic and fractal patterns. 相似文献
12.
Darboux Transformation and Variable Separation Approach: the Nizhnik-Novikov-Veselov Equation 总被引:1,自引:0,他引:1 下载免费PDF全文
Darboux transformation (DT) is developed to systematically find variable separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the one-step DT yields the variable separable solutions, which can be obtained from the truncated Painleve analysis, and the two-step DT leads to some new variable separable solutions, which are the generalization of the known results obtained by using a guess ansatz to solve the generalized trilinear equation. 相似文献
13.
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
14.
ZHANGShun-Li LOUSen-Yue 《理论物理通讯》2003,40(4):401-406
Using the generalized conditional symmetry approach, a complete list of canonical forms for the Korteweg de-Vries type equations with which possessing derivative-dependent functional separable solutions (DDFSSs) is obtained. The exact DDFSSs of the resulting equations are explicitly exhibited. 相似文献
15.
Functional Variable Separation for Generalized (1+2)-Dimensional Nonlinear Diffusion Equations 总被引:1,自引:0,他引:1 下载免费PDF全文
The functional variable separation approach is applied to study the generalized (1 2)-dimensional nonlinear diffusion equations. Complete classification for those equations admitting the functional separable solutions and some such exact solutions are obtained. Consequently, the results reported previously are widely extended. 相似文献
16.
The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics 下载免费PDF全文
Using the projective Riccati equation expansion (PREE) method, new
families of variable separation solutions (including solitary wave
solutions, periodic wave solutions and rational function solutions)
with arbitrary functions for two nonlinear physical models are
obtained. Based on one of the variable separation solutions and by
choosing appropriate functions, new types of interactions between
the multi-valued and single-valued solitons, such as a peakon-like
semi-foldon and a peakon, a compacton-like semi-foldon and a
compacton, are investigated. 相似文献
17.
GOU Ming QU Chang-Zheng 《理论物理通讯》2008,49(2):257-262
We study the functional separation of variables to the nonlinear heat equation: ut = (A(x)D(u)ux^n)x+ B(x)Q(u), Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained. 相似文献
18.
Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients 下载免费PDF全文
In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation. 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.
A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation 下载免费PDF全文
A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein-Gordon equation. 相似文献