Discrete reductive perturbation technique

Abstract

We expand a partial difference equation (PΔE) on multiple lattices and obtain the PΔE which governs its far field behavior. The perturbative-reductive approach is here performed on well-known nonlinear PΔEs, both integrable and nonintegrable. We study the cases of the lattice modified Korteweg-de Vries (mKdV) equation, the Hietarinta equation, the lattice Volterra-Kac-Van Moerbeke equation and a nonintegrable lattice KdV equation. Such reductions allow us to obtain many new PΔEs of the nonlinear Schrödinger type.