  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.
