DIFFERENTIAL INVARIANTS OF A GENERALIZED VARIABLE-COEFFICIENT GARDNER EQUATION

摘要

In this paper, we consider a generalized variable-coefficient Gardner equation. By using the equivalence group of this equation, we derive the differential invariants of first order and the corresponding invariant equations. We employ these differential invariants and invariant equations to find the most general subclass of variable-coefficient Gardner equations which can be mapped into a specific constant-coefficient equation by means of an equivalence transformation. Furthermore, differential invariants are applied to obtain exact solutions.