Abstract: 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 have many things in common.

Key words: bonding imperfection, sensitivity analysis, radial point interpolation method (RPIM), spring-layer model, Hellinger-Reissner (H-R), variational principle