共查询到20条相似文献,搜索用时 0 毫秒
1.
ZHANG Shun-Li ZHU Xiao-Ning WANG Yong-Mao LOU Sen-Yue 《理论物理通讯》2008,49(4):829-832
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations. 相似文献
2.
Variable Separation Solution for (1+1)-Dimensional Nonlinear Models Related to Schroedinger Equation
XUChang-Zhi ZHANGJie-Fang 《理论物理通讯》2004,42(4):568-572
A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately. 相似文献
3.
Using the generalized conditional symmetry approach, we obtain a
number of new generalized
(1+1)-dimensional nonlinear wave
equations that admit derivative-dependent functional separable
solutions. 相似文献
4.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 相似文献
5.
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
6.
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
7.
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 相似文献
8.
Variable Separation for (1 + 1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives 总被引:1,自引:0,他引:1
We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A(u, ux)uxxx + B(u, ux) that admits derivativedependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples. 相似文献
9.
ZHANG Shun-Li 《理论物理通讯》2006,45(6):969-978
The generalized conditional symmetry is developed to study the variable
separation for equations of type uxt=A(u,ux)uxx+B(u,ux). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their
exact separable solutions are constructed. 相似文献
10.
ZHU Jia-Min MA Zheng-Yi 《理论物理通讯》2006,46(3):393-396
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found. 相似文献
11.
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
12.
ZHU Jia-Min MA Zheng-Yi 《理论物理通讯》2006,46(9)
In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2 1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions.Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found. 相似文献
13.
By using a Bäcklund transformation and the multi-linear variable separation approach, we find a new general
solution of a (2+1)-dimensional generalization of the nonlinear
Schrödinger system. The new “universal” formula is defined, and then, rich coherent structures can be found by selecting corresponding
functions appropriately. 相似文献
14.
Solving Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces via an Improved Variable Separation Approach 总被引:1,自引:0,他引:1
LIDe-Sheng LUOCheng-Xin ZHANGHong-Qing 《理论物理通讯》2004,42(1):1-3
Starting from Baecklund 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
15.
In this letter, starting from a B\"{a}cklund transformation, a
general solution of a (2+1)-dimensional integrable system is
obtained by using the new variable separation approach. 相似文献
16.
SHEN Shou-Feng 《理论物理通讯》2005,44(5):779-782
The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less system. Namely, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically. 相似文献
17.
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
18.
Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations 总被引:1,自引:0,他引:1
ZHANG Shun-Li LOU Sen-Yue QU Chang-Zheng YUE Rui-Hong 《理论物理通讯》2005,44(4):589-596
The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed. 相似文献
19.
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
20.
A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献