The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical ...The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical computation of travelling wave solutions for differential difference equations, our method obtains exact solutions which have physical relevance.展开更多
In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformat...In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformation.The solutions of the generalized Toda equations are derived using the tau functions.The relationship between the generalized nonperiodic Toda lattices and Lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices,whose integrability and Darboux transformation are studied.展开更多
基金The project supported by ＂973＂ Project under Grant No.2004CB318000, the Doctor Start-up Foundation of Liaoning Province of China under Grant No. 20041066, and the Science Research Plan of Liaoning Education Bureau under Grant No. 2004F099
文摘The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical computation of travelling wave solutions for differential difference equations, our method obtains exact solutions which have physical relevance.
基金the National Natural Science Foundation of China under Grant No.12071237the K C Wong Magna Fund in Ningbo University。
文摘In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the particles.We obtain the generalized finite nonperiodic Toda equations via a symmetric group transformation.The solutions of the generalized Toda equations are derived using the tau functions.The relationship between the generalized nonperiodic Toda lattices and Lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices,whose integrability and Darboux transformation are studied.
