Exact solutions of non-integrable lattice equations

Abstract

The method of generalized conditional symmetry used by Fokas and Liu for deriving nonintegrable evolution equations which possess exact analytic solutions is here extended to the construction of differential-difference equations supporting two-kink and two-soliton solutions. In particular, we build the discrete analogue of a Burgers type equation with reaction term, investigated in the continuous case by Satsuma, and describing the coalescence of two travelling waves. We also derive the discrete form of a nondispersive evolution equation possessing like the Korteweg-de Vries equation a two-soliton solution.