New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.
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
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
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
基金Supported by the NSF of Henan Province(112300410109)Supported by the NSF of the Education Department(2010A110022)
文摘New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11601247 and 11605096the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos.2016MS0115 and 2015MS0116the Innovation Fund Programme of Inner Mongolia University No.201611155
文摘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.
基金Acknowledgements The first author would like to express her sincere thanks to Prof. Xing-Biao ttu for his helpful discussion and encouragement. This work was supported by the Program of Higher-level Talents of Inner Mongolia University (2011153, 21100-5145101), the National Natural Science Foundation of China (Grant Nos. 11561048, 11547101) and the Natural Science Foundation of Inner Mongolia Autonomous Region (2015MS0116).
文摘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.
基金Supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant No. 07XNA013
文摘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.