On the mKdV-Liouville hierarchy and its self-similarity reduction

TL;DR

This paper explores the relationship between the mKdV-Liouville hierarchy and the mKdV hierarchy, providing solutions and discussing the potential for new transcendental functions derived from their self-similarity reductions.

Contribution

It introduces a novel connection between the mKdV-Liouville and mKdV hierarchies using an extended truncation approach and constructs solutions from known solitons.

Findings

Solutions for the mKdV-Liouville hierarchy derived from mKdV solitons

Potential for defining new transcendental functions from hierarchy reductions

Enhanced understanding of integrable mixed models

Abstract

Integrable mixed models have been used as a generalization of traditional integrable models. However, a map from a traditional integrable model to a mixed integrable model is not well understood yet. Here, it is studied the relation between the mKdV-Liouville hierarchy and the mKdV hierarchy by employing an extended version of the modified truncation approach. This paper shows some solutions for the mKdV-Liouville hierarchy constructed from the soliton solutions of the mKdV hierarchy. The last section deals with the possibility of define new transcendental functions from the self-similarity reduction of the mKdV-Liouville hierarchy.