(2+1)维Kadomtsov-Petviashvili-Joseph-Egri方程的李对称分析和精确解

LIE SYMMETRY ANALYSIS AND EXACT SOLUTION OF (2+1)-DIMENSIONAL KADOMTSOV-PETVIASHVILI-JOSEPH- EGRI EQUATION

利用经典李群方法,得到(2+1)维Kadomtsov-Petviashvili-Joseph-Egri方程的经典李点对称,并利用对称得到该方程的一些相似约化,通过求解约化方程,得到了该方程的很多精确解,包括双曲函数解,雅可比椭圆函数解,三角函数解,有理函数解,幂级数解等。

Based on the classical Lie group method, we obtain the classical Lie point symmetry of the （2＋1）-dimensional Kadomtsov-Petviashvili-Joseph-Egri （KP-JE for short） equation. Using the symmetries, we find some classical similarity reductions of KP-JE equation. Many kinds of exact solutions of the KP-JE equation are derived by solving the reduced equations, including the elliptic functions , the rational functions,the hyperbolic functions, the trigonometric functions, the power series solution.