Classification of traveling wave solutions of the modified Zakharov--Kuznetsov equation

TL;DR

This paper classifies all traveling wave solutions of the modified Zakharov--Kuznetsov equation using a distribution-based integration method, unifying and extending previous ansatz-based approaches.

Contribution

It introduces a distribution-based method for classifying solutions, generalizing prior ansatz-specific results for the modified Zakharov--Kuznetsov equation.

Findings

Complete classification of traveling wave solutions

Unification of previous results

Extension beyond ansatz-based methods

Abstract

The $\mathcal{C}^{\infty}$-structure-based method of integration of distributions of vector fields is used to classify all the traveling wave solutions of the modified Zakharov--Kuznetsov equation. This work unifies and generalizes the particular results obtained in the recent literature by using specific ansatz-based methods.