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1.
For describing various complex nonlinear phenomena in the realistic world, the higher-dimensional nonlinear evolution equations appear more attractive in many fields of physical and engineering sciences. In this paper, by virtue of the Hirota bilinear method and Riemann theta functions, the periodic wave solutions for the (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev Petviashvili (KP) equation are obtained. Furthermore, it is shown that the known soliton solutions for the two equations can be reduced from the periodic wave solutions.  相似文献   

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In this paper, we obtain a 1+1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota's discretization method. A bilinear Backlund transformation and the associated Lax pair are also proposed/or this model.  相似文献   

4.
邓淑芳 《中国物理快报》2006,23(7):1662-1665
The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Backlund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bgcklund transformation.  相似文献   

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In this paper, the investigation is focused on a (3+1)-dimensional variable-coefficient Kadomtsev- Petviashvili (vcKP) equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the (3+1)-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the (3+1)-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.  相似文献   

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吴建平 《中国物理快报》2008,25(12):4192-4194
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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Under investigation in this paper is a(3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials,symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, B¨acklund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.  相似文献   

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2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting to the Hirota bilinear method. In this paper, N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation are obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.  相似文献   

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By truncating the Painleve expansion at the constant level term, the Hirota bilinear form is obtained for a (3+1)-dimensional variable-coefficient Kadomtsev Petviashvili equation. Based on its bilinear form, solitary-wave solutions are constructed via the ε-expansion method and the corresponding graphical analysis is given. Furthermore, the exact solution in the Wronskian form is presented and proved by direct substitution into the bilinear equation.  相似文献   

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In this paper, we will use a simple and direct method to obtain some particular solutions of (2+1)- dimensional and (3+ 1)-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f(x) whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.  相似文献   

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Two Darboux transformations of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka ( CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux trans- formations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.  相似文献   

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In this paper, with the aid of symbolic computation, we present a uniform method for constructing soliton solutions and periodic solutions to (2+1)-dimensional Toda lattice equation.  相似文献   

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Based on the Pfaffian derivative formulae, a Grammian determinant solution for a (3+1)-dimensional soliton equation is obtained. Moreover, the Pfaffianization procedure is applied for the equation to generate a new coupled system. At last, a Gram-type Pfaffian solution to the new coupled system is given.  相似文献   

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