Neumann type integrable reduction for nonlinear evolution equations in 1+1 and 2+1 dimensions
Neumann type integrable reduction for nonlinear evolution equations in 1+1 and 2+1 dimensions
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DOI：
10.1063/1.3266168
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发表时间：
2009-12
影响因子：
1.3
通讯作者：
Jinbing Chen
中科院分区：
文献类型：
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作者：
Jinbing Chen
利用非线性化技术给出了一族新的Neumann型系统，实现了修正的Jaulent-Miodek族的变量分离，并在辛子流形TSN−1上得到了一个新的耦合修正的Kadomtsev-Petviashvili方程.通过两个Casimir函数和Lenard本征值方程的特解，我们推导出Neumann型系统的Lax-Moser矩阵，该矩阵产生运动积分和向量场与TSN−1相切的约束哈密顿量。基于Dirac-Poisson括号和TSN−1上的Lax方程，提出了一种新的系统方法，同时证明了一族Neumann型系统的Liouville可积性.利用Dirac-Poisson括号和生成函数揭示了无穷维可积系统与Neumann型系统之间的显式关系，指出Neumann型系统的相容解产生1+1和2+1维可积非线性系统的有限参数解。
A family of new Neumann type systems is given in view of the nonlinearization technique, realizing the variable separation of the modified Jaulent–Miodek hierarchy and a new coupled modified Kadomtsev–Petviashvili equation on the symplectic submanifold TSN−1. By two Casimir functions and a special solution of the Lenard eigenvalue equation, we deduce the Lax–Moser matrix of the Neumann type systems that yields integrals of motion and the constrained Hamiltonians whose vector fields are tangent to TSN−1. Based on the Dirac–Poisson bracket and a Lax equation on TSN−1, a new systematic way is proposed to prove the Liouville integrability of a family of Neumann type systems synchronously. The Dirac–Poisson bracket and the generating function are used to reveal the explicit relation between infinite dimensional integrable systems and Neumann type systems, and then we point out that compatible solutions of Neumann type systems yield the finite parametric solutions of 1+1 and 2+1 dimensional integrable nonlinear...