Solitary wave solutions to some classes of nonlinear evolution type equations using inverse variational methods

Invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. The reductions carry all the advantages regarding Noether symmetries and double reductions via first integrals or conserved quantities. The examples we consider are nonlinear evolution type equations like the general form of the Fizhugh–Nagumo and KdV–Burgers equations. Some aspects of Painlevé properties of the reduced equations are also obtained.