共查询到20条相似文献,搜索用时 156 毫秒
1.
Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the (3+1)-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated. 相似文献
2.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(5):807-809
The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
3.
ZHENG Chun-Long FEI Jin-Xi 《理论物理通讯》2007,48(4):657-661
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solltary wave solutlons, periodic wave solutions and rational function solutions) with arbitrary functions [or the (2+ 1)-dimensional general/zed Broer-Kaup (GBK) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the (2+1)-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed. 相似文献
4.
LUE Zhuo-Sheng XIE Fu-Ding 《理论物理通讯》2006,46(2):199-202
Seeking exact analytical solutions of nonlinear evolution equations is of fundamental importance in mathematlcal physics. In this paper, based on a constructive algorithm and symbolic computation, abundant new exact solutions of the (2+1)-dimensional dispersive long wave equations are obtained, among which there are soliton-like solutions, mult-soliton-like solutions and formal periodic solutions, etc. Certain special solutions are considered and some interesting localized structures are revealed. 相似文献
5.
YANG Xian-Lin TANG Jia-Shi 《理论物理通讯》2008,50(11):1047-1051
The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the (2+1)-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
6.
Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere 下载免费PDF全文
Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations
with a higher-degree of nonlinear terms are derived from a simple
incompressible non-hydrostatic Boussinesq equation set in atmosphere
and are used to investigate gravity waves in atmosphere. By taking
advantage of the auxiliary nonlinear ordinary differential equation,
periodic wave and solitary wave solutions of the fifth-order
KdV--mKdV models with higher-degree nonlinear terms are obtained
under some constraint conditions. The analysis shows that the
propagation and the periodic structures of gravity waves depend on
the properties of the slope of line of constant phase and atmospheric
stability. The Jacobi elliptic function wave and solitary wave
solutions with slowly varying amplitude are transformed into
triangular waves with the abruptly varying amplitude and breaking
gravity waves under the effect of atmospheric instability. 相似文献
7.
A New Rational Algebraic Approach to Find Exact Analytical Solutions to a (2+1)-Dimensional System 总被引:1,自引:0,他引:1
BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2007,48(5):801-810
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on (2+1)-dimensional dispersive long-wave equation. 相似文献
8.
New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 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.
Abundant new exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered. 相似文献
11.
With the aid of an improved projective approach and a linear variable separation method,new types of variable separation solutions (including solitary wave solutions,periodic wave solutions,and rational function solutions)with arbitrary functions for (2 1)-dimensional Korteweg-de Vries system are derived.Usually,in terms of solitary wave solutions and rational function solutions,one can find some important localized excitations.However,based on the derived periodic wave solution in this paper,we find that some novel and significant localized coherent excitations such as dromions,peakons,stochastic fractal patterns,regular fractal patterns,chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications. 相似文献
12.
Yan-Ze Peng 《Pramana》2005,65(2):177-183
By means of the singular manifold method we obtain a general solution involving three arbitrary functions for the (2+1)-dimensional
KdV equation. Diverse periodic wave solutions may be produced by appropriately selecting these arbitrary functions as the
Jacobi elliptic functions. The interaction properties of the periodic waves are investigated numerically and found to be nonelastic.
The long wave limit yields some new types of solitary wave solutions. Especially the dromion and the solitoff solutions obtained
in this paper possess new types of solution structures which are quite different from the basic dromion and solitoff ones
reported previously in the literature. 相似文献
13.
从可积模型的双线性形式出发,可以得到关于方程场变量或某种势所存在的所有方向都是指数局域的dromion解或除一个方向外指数衰减的“Solitoff”解.以(1+1)维和(2+1)维KdV类型方程为例,对孤子(dromions或“Solitoff”)间的相互作用进行了详细的研究,发现孤子间的相互作用规律与方程的维数和类型无关.只要方程的多孤子解形式符合Hirota标准形式(所有耦合系数均不为零),孤子之间的碰撞是弹性的,否则就是非弹性的
关键词:
可积模型
孤子相互作用
双线性方法 相似文献
14.
The interaction of long (sound) and short (ultrasound) waves propagating in a rarefied monodisperse mixture of a weakly compressible liquid with gas bubbles is considered. Using the multiscale method, the Davey-Stewartson system of equations is derived as a model of two-dimensional interaction. It is shown that, for some values of parameters, this system is reduced to an integrable form (the Davey-Stewartson I equations) and has localized solutions in the form of dromions (exponentially decaying waves of the short-wave envelope). One of the most important properties of dromions is their ability to move according to the law that governs the variations of the boundary conditions set at infinity for the long wave. It is suggested that these solutions be used for controlling the effects of ultrasound on bubbly liquids. 相似文献
15.
ZHENG Chun-Long 《理论物理通讯》2004,41(3):391-396
By means of the standard truncated Painlev\'{e} expansion and a variable
separation approach, a general variable separation solution of the
generalized Burgers system is derived. In addition to the usual
localized coherent soliton excitations like dromions, lumps,
rings, breathers, instantons, oscillating soliton excitations,
peakons, foldons, and previously revealed chaotic and fractal
localized solutions, some new types of excitations --- compacton and
Jacobi periodic wave solutions are obtained by introducing
appropriate lower dimensional piecewise smooth
functions and Jacobi elliptic
functions. 相似文献
16.
17.
R. Radha 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,45(2):317-320
In this paper, we have identified a novel method of
inducing localized solutions in the (2+1) dimensional
nonisospectral nonlinear Schr?dinger (NLS) equation by utilising
the freedom in the system. The new class of localized solutions
includes induced dromions, lump dromions, dipole dromions etc. The
amplitude of the localized solutions generated is found to explode
or decay with time. We have also brought out the interaction of
induced dromions. 相似文献
18.
Coherent soliton structures of the (2+1)-dimensional long-wave-short-wave resonance interaction equation 下载免费PDF全文
The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by the entrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shown that the coherent soliton structures may be dromions, solitoffs, etc. 相似文献
19.
Starting from n line soliton solutions of an integrable (2+1)-dimensional sine-Gordon system, one can find a dromion solution which is localized in all directions for a suitable potential. The dromion structures for a special (2+1)-dimensional sine-Gordon equation are studied in detail. The interactions among dromions are not elastic. In addition to a phase shift, the "shape" and the velocity of these dromions may also be changed after interaction. 相似文献
20.
Some new structures and interactions of solitons for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable
separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our
results. Detailed behaviors of interaction are illustrated both
analytically and in graphically. Our analysis shows that the
interaction properties between two solitons are related to the
form of interaction constant. The form of interaction constant and
the dispersion relationship are related to the form of the seed
solution {u0, v0, w0} in Bäcklund transformation. 相似文献