New Multi-order exact solutions for a class of nonlinear evolution equations

We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our multi-order exact solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.