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1.
Using the extended homogenous balance method, we obtain abundant exact solution structures of a (2+1)-dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order term analysis, the nonlinear transformations of generalized Nizhnik-Novikov-Veselov equation are given first, and then some special types of single solitary wave solution
and the multisoliton solutions are constructed. 相似文献
2.
Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case,
the solitary wave solution to NNV equation are also obtained. 相似文献
3.
The elementary and systematic binary Bell polynomials method is applied to the generalized Nizhnik-Novikov-Veselov (GNNV) equation. The bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the GNNV equation are obtained directly, without too much trick like Hirota's bilinear method. 相似文献
4.
Yan-Ze Peng 《Pramana》2005,64(2):159-169
The extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions to the generalized
Nizhnik-Novikov-Veselov equation. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions
are obtained. The method is applicable to a large variety of non-linear partial differential equations, as long as odd-and
even-order derivative terms do not coexist in the equation under consideration. 相似文献
5.
HUANG Wen-Hua ZHANG Jie-Fang 《理论物理通讯》2004,42(7)
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
6.
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
7.
BAI Cheng-Lin 《理论物理通讯》2004,41(1):15-20
Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, the nonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of single solitary wave solution and the multisoliton solutions are constructed. 相似文献
8.
With the aid of the truncated Painlevé expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters. 相似文献
9.
Starting from the variable separation solution obtained by using the extended homogenous balance method, a new class of combined structures, such as multi-peakon and multi-dromion solution,
multi-compacton and multi-dromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting
appropriate functions. These new structures exhibit novel
interaction features. Their interaction behavior is very similar
to the completely nonelastic collisions between two classical particles. 相似文献
10.
Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed. 相似文献
11.
Lü Zhuo-Sheng 《理论物理通讯》2011,55(1):85-88
Employing a constructive algorithm and the symbolic computation, we obtain a new explicit bi-soliton-like solution of the asymmetric Nizhnik-Novikov-Veselov equation. The solution contains two arbitraryfunctions which indicates that it can model various bi-soliton-like waves. In particular, specially choosing the arbitrary functions, we find some interesting bi-solitons with special shapes, which possess the traveling property of the traditional bi-solitons. We show the evolution of such bi-solitons by figures. 相似文献
12.
Compacton, Peakon, and Foldon Structures in the (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation 总被引:1,自引:0,他引:1
By the use of the extended homogenous
balance method, the Backlund transformation
for a (2+1)-dimensional integrable model, the(2+1)-dimensional
Nizhnik-Novikov-Veselov (NNV) equation, is obtained,
and then the NNV equation is transformed into three
equations of linear, bilinear, and tri-linear forms,
respectively. From the above three equations,
a rather general variable separation solution
of the model is obtained. Three novel class localized structures
of the model are founded by the entrance of two variable-separated
arbitrary functions. 相似文献
13.
BAI Cheng-Jie HAN Ji-Guang WANG Wei-Tao AN Hong-Yong 《理论物理通讯》2008,49(5):1241-1244
The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort. 相似文献
14.
15.
采用行波法约化方程,建立一种变换关系,把求解(3+1)维NizhnikNovikovVeselov(NNV)方程的解转化为求解一维非线性KleinGordon方程的解,从而得到了(3+1)维NNV方程的孤子解和周期解.
关键词:
(3+1)维Nizhnik-Novikov-Veselov方程
非线性Klein-Gordon方程
孤子解
周期解 相似文献
16.
Sen-Yue LOU 《理论物理通讯》1997,27(2):249-252
Starting from an inner parameter-dependent symmetry constraint of the Kadomtsev-Petviashvili (KP) equation, the asymmetric multi-component Davey-Stewartson extension and the asymmetric multi-component modified Nizhnik-Novikov-Veselov extension are obtained. 相似文献
17.
利用分离变量法得到了2+1维Nizhnik-Novikov-Veselov方程包含三个任意函数的精确解.合 适地选择任意函数,该精确解可以是描述所有方向指数局域的dromion相互作用,三个方向 指数局域的‘Solitoff’和dromion相互作用以及线孤子和y周期孤子相互作用的解.对dromi on相互作用从解析和几何两个角度进行了详细地探讨,揭示了一些新的相互作用规律.
关键词:
dromions相互作用
NNV方程
分离变量法 相似文献
18.
RUAN Hang-Yu 《理论物理通讯》2005,43(1):31-38
A variable separation approach is used to obtain exact solutions
of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov
equation. Two of these exact solutions are analyzed to study the
interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The
interactions between a line soliton and a y-periodic soliton are
classified into several types according to the phase shifts due to
collision. There are two types of singular interactions. One is
the resonant interaction that generates one line soliton while the
other is the extremely repulsive or long-range interaction where
two solitons interchange each other infinitely apart. Some new
phenomena of interaction between two dromions are also reported in
this paper, and detailed behaviors of interactions are illustrated both
analytically and graphically. 相似文献
19.
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions. 相似文献
20.
XU Chang-Zhi HE Bao-Gang 《理论物理通讯》2006,46(7)
Extended mapping approach is introduced to solve (2 1)-dimensional Nizhnik-Novikov-Veselov equation.A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation,rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately. 相似文献