本项目一方面寻找非线性波方程的怪波解，另一方面研究具有尖峰孤波的可积系统。对前者致力完善已有的求怪波解的方法，并创建推导怪波解的简便途径，依此发现和获得新的怪波结构，进而考察怪波的动力学特征，达到解释非线性现象的要求。拟研究高维非线性波方程和变系数非线性方程的怪波解。对后者探索具有尖峰孤波的可积系统，研究它的可积性质，如Lax对、Hamiltonian结构、守恒律、潘勒卫测试等。借助广义函数理论给出此类可积系统的解析解，特别是尖峰孤子解为一类重要的弱解。

The rogue wave solutions of nonlinear wave equation are found and integrable system with peakon solutions are studied in this work. For the former topic we try to improve the known methods to solving the rogue wave solution and establish the simple approach to deriving the rogue wave solution. We can obtain the novel rogue wave structures and observe the dynamic behaviors of rogue wave phenomenon. For the latter topic we search integrable system with peakon solution and investigate its integrablity, such as Lax pair, Hamiltonian structure, conservation law, Painléve test, and so on. With the help of distribution theory, we give analytic solutions of these integrable system, in which peakon solution is a kind of important weak solution.