一类广义浅水波方程的新精确解
New Exact Solutions of a Generalized Shallow Water Wave Equation
摘要：
本文提出了一种推广的椭圆函数方法，并将其应用于广义浅水波方程。本文系统地研究了用拟周期椭圆积分函数和双周期雅可比椭圆函数表示的新的精确行波解的分类问题。导出的新解包括有理解、周期解、奇异解和孤波解。一个有趣的比较与规范的程序。在某些情况下，所得到的椭圆解在整个空间的某个区域上具有奇异性。对于这样的解决方案，我们已经计算出的有效区域，所获得的解决方案是免费的，从这样的奇异性。
英文摘要：
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic elliptic integral function and doubly-periodic Jacobian elliptic functions. The derived new solutions include rational, periodic, singular and solitary wave solutions. An interesting comparison with the canonical procedure is provided. In some cases the obtained elliptic solution has singularity at certain region in the whole space. For such solutions we have computed the effective region where the obtained solution is free from such a singularity.
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