Cartan's structure of symmetry pseudo-group and coverings for the r-th modified dispersionless Kadomtsev--Petviashvili equation

TL;DR

This paper derives new coverings for the r-th modified dispersionless KP equation using Maurer--Cartan forms and establishes Bäcklund transformations between these coverings, advancing the understanding of its symmetry structure.

Contribution

It introduces two non-equivalent coverings for the r-th mdKP equation and finds Bäcklund transformations connecting them, based on symmetry pseudo-group analysis.

Findings

Derived two non-equivalent coverings for the r-th mdKP equation.

Established Bäcklund transformations between the coverings.

Abstract

We derive two non-equivalent coverings for the r-th mdKP equation from Maurer--Cartan forms of its symmetry pseudo-group. Also we find B\"acklund transformations between the covering equations.