共查询到20条相似文献,搜索用时 15 毫秒
1.
For a special coupled mKdV system, which can be derived from a two-layer fluid model, Hirota's bilinear direct method is used to construct and yield the complexiton solutions. The detailed physical properties of complexitons are filrther illustrated graphically. 相似文献
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N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation 下载免费PDF全文
We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg-de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Backlund transformation between the ( N - 1)- and N-soliton solutions is verified. 相似文献
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Using a complete discrimination system for polynomials and elementary integral method, we obtain the travelling solutions for triple sine-Gordon equation. This method can be applied to similar problems and has general meaning. 相似文献
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Via the elementary Darboux transformation (DT) of the modified Kadomtsev--Petviashvili (mKP) equation, a binary Darboux transformation (BDT) of the mKP equation is constructed. 相似文献
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Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg--de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation 总被引:1,自引:0,他引:1 下载免费PDF全文
Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries (KdV) equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws. 相似文献
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Using the tanh method and a variable separated ordinary difference equation method to solve the double sineGordon equation, we derive some new exact travelling wave solutions, especially a new type of noncontinuous solitary wave solutions. These noncontinuous solitary wave solutions are verified by using the conservation law theory. 相似文献
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Exact Analytic N-Soliton-Like Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics 总被引:2,自引:0,他引:2 下载免费PDF全文
Applicable in fluid dynamics and plasmas, a generalized variable-coefficient Korteweg-de Vries (vcKdV) model is investigated. The bilinear form and analytic N-soliton-like solution for such a model are derived by the Hirota method and Wronskian technique. Additionally, the bilinear auto-Bǎcklund transformation between (N-1)- soliton-like and N-soliton-like solutions is verified. 相似文献
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U. Al Khawaja 《Physics letters. A》2009,373(31):2710-2716
We consider a general form of the Gross-Pitaevskii equation with time- and space-dependent effective mass, external potential and strength of interatomic interaction. Using the inverse-scattering method, we derive the integrability condition of this equation within a general scheme that can be used to find exact solutions of a wide range of linear and nonlinear partial differential equations. We use this condition to derive exact solitonic solutions of the one-dimensional time-dependent Gross-Pitaevskii equation corresponding to a Bose-Einstein condensate trapped by a periodic potential. Both attractive and repulsive interatomic interactions are considered. The values of the parameters of the potential can be chosen such that the periodic potential becomes almost identical to that of an optical lattice. 相似文献
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A Bilinear Backlund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation 下载免费PDF全文
Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation. As an application, soliton solution and stationary rational solution for the (3+1)- dimensional soliton equation are presented. 相似文献
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In this Letter, a few new types of interaction solutions to the KdV equation are obtained through a constructed Wronskian form expansion method. The method takes advantage of the forms and structures of Wronskian solutions to the KdV equation, and the functions used in the Wronskian determinants don't satisfy the systems of linear partial differential equations. 相似文献
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Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation 总被引:2,自引:0,他引:2 下载免费PDF全文
Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtadned. 相似文献
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The multiple soliton solutions of the approximate equations for long water waves and soliton-like solutions for the dispersive
long-wave equations in 2+1 dimensions are constructed by using an extended homogeneous balance method. Solitary wave solutions
are shown to be a special case of the present results. This method is simple and has a wide-ranging practicability, and can
solve a lot of nonlinear partial differential equations. 相似文献
18.
H.C. Hu 《Physics letters. A》2009,373(20):1750-1753
New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation are constructed by means of the Darboux transformation with constant seed solution. The new positon, negaton and complexiton solutions are analytical or singular and given out both analytically and graphically. 相似文献
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With a view to exploring new soliton-like solutions of certain types of nonlinear diffusion-reaction (DR) equations with a variable coefficient, we demonstrate the viability of a method which is the combination of both the symbolic computation technique of Gao and Tian [Y.T. Gao, B. Tian, Comput. Phys. Commun. 133 (2001) 158] and auxiliary equation method of Sirendaoreji [Sirendaoreji, Phys. Lett. A 356 (2006) 124] and used recently for the KdV equation. In particular, the DR equations with quadratic and cubic nonlinearities with a time-dependent velocity in the convective flux term are studied and the existence of soliton-like solutions is shown. 相似文献
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ZHANG Da-Jun 《中国物理快报》2007,24(11):3021-3023