Quasi-Periodic Solutions of (3+1) Generalized BKP Equation By Using Riemann Theta Functions

TL;DR

This paper develops quasi-periodic wave solutions for the (3+1) generalized BKP equation using Riemann theta functions, including one, two, and three periodic solutions, and analyzes their asymptotic behavior towards soliton solutions.

Contribution

It introduces a method to construct multi-periodic solutions for the (3+1) generalized BKP equation using Riemann theta functions, overcoming previous computational difficulties.

Findings

Constructed one, two, and three periodic wave solutions.

Analyzed the asymptotic behavior of solutions towards solitons.

Extended the application of Riemann theta functions to complex higher-dimensional equations.

Abstract

This paper is focused on quasi-periodic wave solutions of (3+1) generalized BKP equation. Because of some difficulties in calculations of N=3 periodic solutions, hardly ever has there been a study on these solutions by using Rieamann theta function. In this study, we obtain one and two periodic wave solutions as well as three periodic wave solutions for (3+1) generalized BKP equation. Moreover we analyse the asymptotic behavior of the periodic wave solutions tend to the known soliton solutions under a small amplitude limit.