具有新四阶项的非线性微分方程的精确解

Exact solutions of nonlinear differential equations with new fourth-order terms

研究了一类具有新的四阶项D_(x)^(2)D_(T)^(2)非线性偏微分方程的问题,其中三个新的四阶导数项和一些二阶导数项增加了非线性方程求解的困难.构造非线性偏微分方程的Hirota双线性形式,利用Hirota双线性方法得到方程的Lump解.通过绘图分析了它们的动力学行为.

A nonlinear PDE combining with a new fourth-order term D_(x)^(2)D_(T)^(2)was studied.Adding three new fourth-order derivative terms and some second-order derivative terms,it increased difficulty in solving.This paper formulated a combined fourth-order nonlinear partial differential equation,which possesses a Hirota s bilinear form.The class of lump solutions were constructed explicitly through the Hirota s bilinear method.The dynamical behaviors were analyzed through plots.