Localized excitation on the Jacobi elliptic periodic background for the (n+1)-dimensional generalized Kadomtsev-Petviashvili equation

TL;DR

This paper investigates localized nonlinear wave solutions on Jacobi elliptic function backgrounds for the (n+1)-dimensional generalized Kadomtsev-Petviashvili equation, revealing diverse wave types and dynamics influenced by spectral parameters.

Contribution

It introduces novel local nonlinear wave solutions using Darboux transformation on Jacobi elliptic backgrounds for the gKP equation, expanding understanding of wave dynamics in higher dimensions.

Findings

Existence of soliton and breather solutions with various spectral parameters

Effect of nonlinearity and dispersion on breather wave propagation

Degenerate solutions at specific Jacobi function moduli (0 and 1)

Abstract

In this paper, the linear spectral problem, which associated with the (n+1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, with the Jacobi elliptic function as the external potential is investigated based on the Lam\'{e} function, from which some novel local nonlinear wave solutions on the Jacobi elliptic function have been obtained by Darboux transformation, and the corresponding dynamics have also been discussed. The degenerate solutions of the nonlinear wave solutions on the Jacobi function background for the gKP equation are constructed by taking the modulus of the Jacobi function to be 0 and 1. The findings indicate that there can be various types of nonlinear wave solutions with different ranges of spectral parameters, including soliton and breather waves. Furthermore, the interplay between nonlinearity and dispersion is found to have observable effects on the propagation dynamics of breather waves. These results will be useful for elucidating and predicting nonlinear phenomena in related physical fields, such as fluid mechanics and physical ocean.