Hyperelliptic Function Solutions of Three Genus for KP Equation Using Direct Method

Abstract

In this paper, we will use a simple and direct method to obtain some particular solutions of (2 + 1)-dimensional and (3 + 1)-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y2 = f(x) whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.