Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

TL;DR

This paper derives solitary wave solutions for the KP, cylindrical KP, and spherical KP equations by transforming them into the KdV equation, leveraging known solutions to obtain explicit solitary wave solutions.

Contribution

It introduces a method to find solitary wave solutions of three (2+1)-dimensional KP-related equations via transformation to the KdV equation, providing explicit solutions.

Findings

Explicit solitary wave solutions for KP, cylindrical KP, and spherical KP equations.

Unified approach simplifies solving complex (2+1)-dimensional equations.

Solutions demonstrate the wave behaviors in different geometrical contexts.

Abstract

Three (2+1)-dimensional equations, they are KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully.