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Applied Mathematics and Mechanics

, Volume 8, Issue 9, pp 853–860 | Cite as

On discontinuous periodic solution and discontinuous solitary wave of two-dimension shallow water equation

  • Huang Si-xun
Article

Abstract

In this paper we discuss discontinuous periodic solution and discontinuous solitary wave of the shallow water model of geophysical fluid dynamics. When we consider the properties of trajectory near non-equilibrium point, i.e. singular point, we find that if we introduce the concept of generalized solution (piecewise smoothing continuous solution), then the system will produce discontinues periodic solution and the condition of discontinuous periodic solution can he 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.

Keywords

Atmosphere Mathematical Modeling Fluid Dynamic Generalize Solution Periodic Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Huang Si-xun, Nonlinear gravity inertial wave of two dimensions and discussing the possibility of solitary wave's existence. (to appear)Google Scholar
  2. [2]
    Sansone, G. and R. Conti,Nonlinear Differential Equation, Pergamon Press (1964).Google Scholar

Copyright information

© Shanghai University of Technology 1987

Authors and Affiliations

  • Huang Si-xun
    • 1
  1. 1.Meteorological Institute of Air ForceNanjing

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