Similarity transformations and linearization for a family of dispersionless integrable PDEs

Abstract

We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlevé transcendents. The main results of this study is that from the application of the similarity transformations provided by the Lie point symmetries all the members of the family of the partial differential equations are reduced to second-order differential equations which are maximal symmetric and can be linearized.

15 pages, no figues

References in corpus (3)

• Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models
• One-dimensional optimal system for 2D Rotating Ideal Gas
• Lie symmetries of two-dimensional shallow water equations with variable bottom topography