非线性Pochhammer－Chree方程的行波解

讨论了广义非线性Ｐｏｃｈｈａｍｍｅｒ－Ｃｈｒｅｅ方程行波解的存在性，该方程具有广泛的物理。力学背景。通过对相应常微分方程解的存在性及其性态的研究，得到了Ｐｏｃｈｈａｍｍｅｒ－Ｃｈｒｅｅ方程的孤立于行波解之存在性，给出了当非线性项为多项式型时方程孤立子解的显示表示。另外，对常微分方程建立的一些结论亦有独立存在意义。显然本文中方法可用于其它一些非线性数学、物理模型行波解存在性的讨论上。

Travelling Wave Solutions for the Nonlinear Pochhammer-Chree Equation

This paper aims at searching out the existence of travelling wave solutions for the nonlinear Pochhammer-Chree equation.It is known that this equation has a strong background in both physics and mechanirs.The soliton-like travelling wave solutions for the nonlinear Pochhammer-Chree equation are obtained by comparing the existence and asymptotic behavior of solutions to the corresponding ordinary differential equations.The explicit expression of solitary solutions to the equation with power nonlinearity is given as well.Furthermore,some conclusions in this paper for ordinary differential equations are also of significance,and the method being introduced is applicable to other physical models.