奇波和怪波模型的动力学性质研究

By using the theory of singular nonlinear traveling wave systems developed by [5], for some nonlinear wave equations which have important physical background, we study the existence of solitary waves, periodic waves, peakons and compactons and find exact solutions and their bifurcations; For some models which there exist homoclinic rogue waves, we develop the method of Melnikov analysis, derive the criteria of persistence of homoclinic solutions, i.e., investigate the chaotic regime of rogue wave formation.

应用文[5]发展的奇非线性行波方程理论，研究系列有重要物理意义的非线性波方程的孤立波、周期波、孤立尖波和紧波解的分支和精确参数表示; 发展无穷维动力系统的Melnikov分析方法，研究某些重要怪波模型的同宿解在扰动下的持续性判据和必要条件.

应用申请者所发展的奇非线性行波方程理论，研究系列有重要物理意义的非线性波方程的孤.立波、周期波、孤立尖波和紧波解的分支和精确参数表示; 发展无穷维动力系统的Melnikov分.析方法，研究某些重要怪波模型的同宿解在扰动下的持续性判据和必要条件.