一类非线性发展方程行波解的不稳定性

Instability of traveling waves of nonlinear evolution equation

利用tanh函数与计算机代数,可以找到许多具有实际背景的非线性发展方程精确行波解的存在性,但对它们稳定性的研究,目前还很少见.利用谱分析与半群理论的方法,对一类描述浅水波在对流中运动的非线性发展方程,就其行波解的非线性不稳定性进行详细的讨论,并得到其行波解在H2(R)扰动下的非线性不稳定性.

Using the tanh function and the computer algebra, the precise traveling wave solutions of many nolinear evolution equations with the actual background may be found. But it is rare to the research of their stability at present. In this paper the spectrum analysis and the semi-group theory method was used to study the instability of the traveling waves of nonlinear evolution equation of surface waves in a convecting fluid. And it proves that the traveling waves are nonlinearly unstable under H2 （R） perturbations.