广义Broer-Kaup-Kupershmidt孤子方程的拟周期解

Quasi-Periodic Solution of the Generalized Broer-Kaup-Kupershmidt Soliton Equation

该文从新谱问题出发,得到一个新的(2+1)-维广义Broer-Kaup-Kupershmidt孤子方程在Lax对非线性化下被分解成可积的常微分方程.接着,给出了一个有限维Hamilton系统并且证明在Liouville意义下是完全可积的.通过引进Abel-Jacobi坐标把Hamilton流进行了拉直,借助Riemannθ函数得到了(2+1)-维Broer-Kaup-Kupershmidt孤子方程的拟周期解.

In this paper,starting from a new spectral problem,a new（2 ＋ 1）-dimensional generalized Broer-Kaup-Kupershmidt soliton equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of Lax pairs.Then,a finitedimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense.The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows,from which the quasi-periodic solution of the（2 ＋ 1）-dimensional generalized Broer-KaupKupershmidt soliton equation is obtained in terms of Riemann theta functions.