二维浅水波方程的间断周期解和间断孤立波解讨论

本文讨论地球流体运动浅水波模式中间断周期解与间断孤立波解.在系统的非平衡点即奇点附近考虑轨线性质时,我们发现只要引入广义解的概念(分片光滑连续解),就会产生间断周期解并得到了间断周期解的条件.当系统在退化的过程中,发现系统此时会产生间断的孤立波解,与此同时其它物理量也产生了间断.这里我们发现,一般认为在超高速情况下解会产生间断,然而在非超高速时也会产生间断现象.本文讨论了上述一系列问题得到了间断解的解析解表达式,并把这一事实与飑线的实例进行比较,得到了不少类似之处.

On Discontinuous Period Solution and Discontinuous Solitary Wave of Two-Dimension Shallow Water Equation

In this paper we discuss discontiunuous periodic solution and discontinuous solitary wave of the shallow water model of geophysical fluid dynamics. When we consider the properties of trajectory near non-equiubrium point, i.e. singular point, we find that if we introduce the concept of generalized solution(pieccwise smoothing continuous solution), then the system will produce disdontinuous periodic solution and the condition of discontinuous periodic solution can be obtained. When the system is degenerated, we find that the discontinuous solitary wave is existent in the system. In this paper we consider a series of problems and obtain analytic expression of discontinuous solution. This result is compared with squall line in the atmosphere, and both of them are similar.