Differential equations invariant under conditional symmetries

TL;DR

This paper develops a method to construct nonlinear PDEs that possess specific conditional symmetries by using invariants of the symmetry generator and additional characteristic conditions, demonstrated through examples like Boussinesq and KdV equations.

Contribution

It introduces a systematic approach to derive nonlinear PDEs with prescribed conditional symmetries using invariants and characteristic conditions.

Findings

Constructed new classes of nonlinear PDEs with conditional symmetries.

Demonstrated methodology with examples including Boussinesq and KdV equations.

Showed how to impose extra symmetry conditions to generate invariant equations.

Abstract

Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry. Several of examples starting from the Boussinesq and including non-autonomous Korteweg-De Vries like equations are given to showcase the methodology introduced.