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1.
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
2.
Complex wave excitations general (2+1)-dimensional and chaotic patterns for a Korteweg-de Vries system
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Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for a general (2+1)-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system (GKdV) is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV 相似文献
3.
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions. 相似文献
4.
With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition. 相似文献
5.
通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
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8.
The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics
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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
9.
Davood Momeni 《Physics letters. A》2019,383(14):1543-1548
We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge. 相似文献
10.
PENG Yan-ze 《理论物理通讯》2003,40(9)
A new Backlund transformation for (2 1)-dimensional KdV equation is first obtained by using homogeneousbalance method. And making use of the Backlund transformation and choosing a special seed solution, we get specialtypes of solitary wave solutions. Finally a general variable separation solution containing two arbitrary functions isconstructed, from which abundant localized coherent structures of the equation in question can be induced. 相似文献
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12.
A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear
partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages
of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered
and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function
solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational
solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is
shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial
differential equations. 相似文献
13.
《Journal of Nonlinear Mathematical Physics》2013,20(2):117-125
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa–Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u-1(c), where c is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa–Holm equation. However, the two component Camassa–Holm equation has distinct from Camassa–Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of u-1(c) is not zero. We provide examples of such solutions. 相似文献
14.
PENGYan-Ze 《理论物理通讯》2003,40(3):257-258
A new Baecklund transformation for (2 1)-dimensional KdV equation is first obtained by using homogeneous balance method. And making use of the Baecklund transformation and choosing a special seed solution, we get special types of solitary wave solutions. Finally a general variable separation solution containing two arbitrary functions is constructed, from which abundant localized coherent structures of the equation in question can be induced. 相似文献
15.
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic. 相似文献
16.
CHEN Yong WANG Qi LI Biao 《理论物理通讯》2004,42(9)
Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1 1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions. 相似文献
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Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of \((3\,{+}\,1)\)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures. 相似文献
19.
In this article, the novel (G ′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed. 相似文献
20.
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