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New Type of Variable-coefficient KP Equation with Self-consistent Sources and Its Grammian Solutions
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作者 XING Xiu-zhi LIU Yan-wei 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第1期152-158,共7页
New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.
关键词 source generation procedure variable-coefficient KP equation hipota’s bilinear method grammian solution
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Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation
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作者 Gegenhasi Ya-Qian Li Duo-Duo Zhang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第4期357-366,共10页
In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference ... In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the m KP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a B?cklund transformation for the differentialdifference KP equation with self-consistent sources. 展开更多
关键词 modified differential-difference KP equation source generation procedure determinant solution Backlund transformation
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Discrete three-dimensional three wave interaction equation with self-consistent sources
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作者 Gegenhasi Zhaowen YAN 《Frontiers of Mathematics in China》 SCIE CSCD 2016年第6期1501-1513,共13页
A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarifi... A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarified by presenting its discrete Gram-type determinant solution. It is shown that the discrete three-dimensional three wave interaction equation with self-consistent sources has a continuum limit into the three-dimensional three wave interaction equation with self-consistent sources. 展开更多
关键词 Discrete three-dimensional three wave interaction equation self-consistent sources source generalization procedure discrete Gram-type determinant
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A New Generalized System on the Two-Dimensional Toda Lattice and Its Reduction
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作者 朱国庆 王红艳 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第2期137-140,共4页
In this paper, we apply the source generation procedure to the coupled 2D Toda lattice equation (also called Pfaffianized 2D Toda lattice), then we get a more generalized system which is the coupled 2D Toda lattice ... In this paper, we apply the source generation procedure to the coupled 2D Toda lattice equation (also called Pfaffianized 2D Toda lattice), then we get a more generalized system which is the coupled 2D Toda lattice with self-consistent sources (p-2D TodaESCS), and a pfaman type solution of the new system is given. Consequently, by using the reduction of the pfaffian solution to the determinant form, this new system can not only be reduced to the 2D TodaESCS, but be reduced to the coupled 2D Toda lattice equation. This result indicates that the p-2D TodaESCS is also a pfafilan version of the 2D TodaESCS, which implies the commutativity between the source generation procedure and Pfaffianization is valid to the semi-discrete soliton equation. 展开更多
关键词 2D Toda lattice equation source generation procedure PFAFFIANIZATION
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