非线性强度下浅水波方程的尖峰孤立子解

Peaked soliton solutions of shallow water wave equations on nonlinear strength

引入非线性强度浅水波方程,研究了该类方程中非线性强度项m对方程解的影响.对m的不同取值得到了方程的尖峰孤立子解,特别是二类新型尖峰孤立子解,此新解不同于通常的e-|x-ct|型的尖峰孤立波解,且解是非局部的,可以表示为δ函数的形式,并给出相应解的图形.同时,对浅水波方程中的常系数γ进行了讨论,得到γ>0,γ<0下不同类型的非线性强度浅水波方程的孤立波解.

The nonlinear strength in shallow water wave equations is studied. The influence of the nonlinearity on the solutions of the equation is considered. Peaked soliton solutions on the different values of m, especially the two new peakons are obtained, which are different from the soliton solutions of the form e^-|x-ct| . The new solutions are nonlocal and can be reduced to the function of δ. The corresponding fi-~gures are also given. The constant γ ,and the peaked solutions with the different case of γ>0 and γ<0, are obtained.