A mixed symmetric Painlevé III -V model which describes a hybrid of both equations is defined and obtained by successive self-similarity and Dirac Lagrange multiplier reductions from an integrable 4-boson hierarchy.

Exact rational solutions of the generalized Hunter-Saxton equation are obtained using Padé approximant approach for the traveling-wave and self-similarity reduction. A larger class of algebraic solutions are also obtained by extending a range of parameters within the solutions obtained by this approach.

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Padé approximants for solving nonlinear partial differential equations without requiring a one-dimensional reduction. This method is applied to the λφ 4 model in 4 dimensions and new solutions are obtained.

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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.