A note on nonlinear diffusive equations on Poincar\'e half plane

TL;DR

This paper derives explicit solutions for nonlinear diffusive equations on the Poincaré half-plane using the invariant subspace method, enhancing understanding of their structure and solution techniques.

Contribution

It introduces exact solutions for nonlinear diffusive equations on the Poincaré half-plane via the generalized separation of variables, linking results to the invariant subspace method.

Findings

Exact solutions obtained for specific nonlinear diffusive equations.

Clarification of the role of invariant subspaces in solution structure.

Method demonstrates potential for solving similar equations on curved geometries.

Abstract

In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the context of the general theory of the invariant subspace method.