Conservation laws and line soliton solutions of a family of modified KP equations

TL;DR

This paper investigates a family of modified KP equations, deriving explicit line soliton solutions and conservation laws, and compares their properties in integrable and non-integrable cases.

Contribution

It provides explicit solutions and conservation laws for a broad family of modified KP equations, including non-integrable cases, expanding understanding beyond the classical integrable scenario.

Findings

Explicit line soliton solutions derived for all family members.

All low-order conservation laws identified and compared.

Differences highlighted between integrable and non-integrable cases.

Abstract

A family of modified Kadomtsev-Petviashvili equations (mKP) in 2+1 dimensions is studied. This family includes the integrable mKP equation when the coefficients of the nonlinear terms and the transverse dispersion term satisfy an algebraic condition. The explicit line soliton solution and all conservation laws of low order are derived for all equations in the family and compared to their counterparts in the integrable case.