深水表面波可积发展方程的行波解与分支

摘要

In this paper, we investigate the traveling wave solutions of a small-aspect-ratio wave equation and an integrable evolution equation for surface waves in deep water. By applying the qualitative theory of differential equations, we analyze the phase portraits of the traveling wave systems and obtain the exact explicit representations of solitary wave solutions.%本文研究了small-aspect-ratio波方程和深水表面波可积发展方程的行波解问题。利用微分方程定性理论的方法，分析了行波系统的相图分支，获得了孤立波解的精确表达式。