DECOMPOSITION OF （1＋1）-DIMENTIONAL,（2W1）-DIMENTIONAL SOLITON EQUATIONS AND THEIR QUASI-PERIODIC SOLUTIONS

• 作者: Qian Li Xuemei Li
• 来源期刊: 应用数学年刊：英文版
• 学科: 数学
• 关键词: 数学分析 数学理论 应用数学 函数
• 年，卷（期）: 2015,（3）
• 页码范围: 297-312
• 页数: 16页
• 分类号: O1

摘要

A new spectral problem is proposed, and nonlinear differential equations of the corresponding hierarchy are obtained. With the help of the nonlinearization approach of eigenvalue problems, a new finite-dimensional Hamiltonian system on R2 nis obtained. A generating function approach is introduced to prove the involution of conserved integrals and its functional independence, and the Hamiltonian flows are straightened by introducing the Abel-Jacobi coordinates. At last, based on the principles of algebra curve, the quasi-periodic solutions for the corresponding equations are obtained by solving the ordinary differential equations and inversing the Abel-Jacobi coordinates.