Variable Separation and Exact Solutions for the Kadomtsev-Petviashvili Equation

Lili Song^1*, Yadong Shang²

¹School of Science, Southwest University of Science and Technology, Mianyang, China.
²School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, China.

DOI: 10.4236/apm.2015.53014                

Abstract

In the paper, we will discuss the Kadomtsev-Petviashvili Equation which is used to model shallow-water waves with weakly non-linear restoring forces and is also used to model waves in ferromagnetic media by employing the method of variable separation. Abundant exact solutions including global smooth solutions and local blow up solutions are obtained. These solutions would contribute to studying the behavior and blow up properties of the solution of the Kadomtsev-Petviashvili Equation.

Keywords

Kadomtsev-Petviashvili Equation, Method of Variable Separation, Global Smooth Solution, Local Blow up Solution

Conflicts of Interest

The authors declare no conflicts of interest.

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