Camassa-Holm型方程的相关研究

本项目主要研究Camassa-Holm（CH）型方程的反向变换、双Hamilton结构、尖峰解的求解问题以及新的2+1、3+1维CH型方程的构造。 即研究若干谱问题已知的CH型方程的双哈密顿结构；利用reciprocal变换建立若干CH型方程与已知具有物理意义的经典系统之间的联系；利用三哈密顿对偶方法构造一些新的高维CH型方程并得到其谱问题；求解若干CH型方程多尖峰解。

The project is mainly focused on reciprocal transformations and bi-Hamiltonian structures as well as peakon solutions of Camassa-Holm(CH) type equations, and construction of some new 2+1，3+1 dimensional CH type equations. It contains getting bi-Hamiltonian structures of some CH type equations which spectral problems are known; constructing reciprocal transformations for some CH type equations to connect the equations with some classical integrable systems admitting physically significant; obtaining some new high-dimensional CH type equations and their spectral problems by tri-Hamiltonian duality method, solving the multi-peakon solutions of some CH type equations.