一类耦合浅水波方程的解析求解和应用分析

The Analytical Solution and Application of a Coupled Shallow Water Wave Equation

本文通过解析方法求解了一类耦合的非线性浅水波方程并对所得解进行了讨论。研究了不同参数情况下方程解的行为,结论表明频散系数可明显影响浅水波方程的动力学。基于本文给出的方程,讨论了其在特殊参数下的一些拓展应用。本文的结论对浅水波方程有关性质的研究具有一定参考意义。

In this paper, solutions of a set of coupled nonlinear shallow water wave equations are solved based on the analytical method, and the results are discussed. The behavior of the equation solution un-der different parameters is studied. We concluded that the dispersion coefficient can significantly affect the dynamics of the shallow water wave. Based on the equations given in this paper, some ex-tended applications under special parameters are discussed. The result presented in this paper may give insights to the relevant studies of the shallow water wave equation.