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

• It was shown the relation between the mKdV and mKdV–Liouville hierarchies.
• Exact solutions for the mKdV–Liouville hierarchy was obtained.
• New solutions for the mKdV hierarchy was obtained.
• The self-similarity reduction of the mKdV–Liouville was studied.

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.