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1.
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
2.
SHEN Shou-Feng 《理论物理通讯》2005,44(11)
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
3.
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
4.
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
5.
SHEN Shou-Feng PAN Zu-Liang ZHANG Jun 《理论物理通讯》2004,42(10)
The variable separation approach method is very useful to solving (2 1 )-dimensional integrable systems. But the (1 1)-dimensional and (3 1 )-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1 1) dimensions by taking the Redekopp system as a simple example and (3 1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3 1 )-dimensional universal formula obtained from many (2 1 )-dimensional systems is extended. 相似文献
6.
XU Chang-Zhi 《理论物理通讯》2006,46(3):403-406
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately. 相似文献
7.
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
8.
SHENShou-Feng PANZu-Liang ZHANGJun 《理论物理通讯》2004,42(4):565-567
The variable separation approach method is very useful to solving (2 1)-dimensional integrable systems.But the (1 1)-dimensional and (3 1)-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1 1) dimensions by taking the Redekopp system as a simp!e example and (3 1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3 1)-dimensional universal formula obtained from many (2 1)-dimensional systems is extended. 相似文献
9.
XU Chang-Zhi 《理论物理通讯》2006,46(9)
Variable separation approach is introduced to solve the (2 1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately. 相似文献
10.
In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1 1)-dimensional and (3 1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1 1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3 1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables. 相似文献
11.
We study the localized coherent structures ofa generally nonintegrable (2 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution. 相似文献
12.
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
13.
14.
Variable separation solutions and new solitary wave structures to the (l+l)-dimensional Ito system
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A variable separation approach is proposed and extended to the
(1+1)-dimensional physics system. The variable separation solution of
(1+1)-dimensional Ito system is obtained. Some special types of solutions
such as non-propagating solitary wave solution, propagating solitary wave
solution and looped soliton solution are found by selecting the arbitrary
function appropriately. 相似文献
15.
16.
In this letter, using a Bäcklund transformation and the new
variable separation approach, we find a new general solution of
the (N+1)-dimensional Burgers system. The form of the universal
formula obtained from many (2+1)-dimensional system is extended. 相似文献
17.
SHENShou-Feng PANZu-Liang ZHANGJun 《理论物理通讯》2004,42(1):49-50
In this Letter, using Ba^ecklund transformation and the new variable separation approach, we find a new general solution to the (3 1)-dimensional Burgers equation. The form of the universal formula obtained from many (2 1)-dimensional systems is extended. Abundant localized coherent structures can be found by seclecting corresponding functions appropriately. 相似文献
18.
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
19.
New periodic wave solutions,localized excitations and their interaction for (2+l)-dimensional Burgers equation
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Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+l)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). 相似文献
20.
The variable separation approach is used to obtain localized coherent structures of the new (2 1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks. 相似文献