(2+1)维广义柱Kadomtsev-Petviashvilli方程的Painlevé分析及精确解

将Painlevé分析的WTC方法应用到高维变系数方程中,并以(2+1)维广义变系数KP方程为例,得到精确解;首先对(2+1)维广义柱Kadomtsev-Petviashvilli方程进行Painlevé分析,确定Painlevé展开式,其次确定共振点,验证共振点,进行相容性分析,最后给出新形式的精确解及其解的图像,在此基础上,再利用G′/G展开法,得到该方程新的一般形式的精确解,并讨论特殊情况下该方程的一组特解,扩大解的范围,使方程的解更加完善.

(2+1)维变系数Kadomtsev-Petviashvilli方程新的精确解

很多自然界重要的复杂物理现象都能用非线性发展方程来表达,求解非线性方程的精确解已经变得越来越重要,各类求解精确解的方法不断被研究者提出。利用推广后的G′/G展开法,结合Mathematical软件对(2+1)维变系数Kadomtsev-Petviashvilli方程进行了求解,获得(2+1)维变系数Kadomtsev-Petviashvilli方程的用双曲函数和三角函数表示的精确解。

Solitary Wave Solutions to the ZKBBM Equation and the KPBBM Equation via the Modified Simple Equation Method

In this article, the modified simple equation method （MSE） is used to acquire exact solutions to nonlinear evolution equations （NLEEs） namely the Zakharov- Kuznetsov Benjamin-Bona-Mahony equation and the Kadomtsov-Petviashvilli Benjamin-Bona-Mahony equation which have widespread usage in modern science. The MSE method is ascending and useful mathematical tool for constructing exact travel- ing wave solutions to NLEEs in the field of science and engineering. By means of this method we attained some significant solutions with free parameters and for special values of these parameters, we found some soliton solutions derived from the exact solutions. The solutions obtained in this article have been shown graphically and also discussed physically.