Discrete Reductive Perturbation Technique

Abstract

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

18 pages, 1 figure. submitted to Journal of Mathematical Physics

References in corpus (2)

• A new two-dimensional lattice model that is "consistent around a cube"
• Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV

Cited by in corpus (7)

• A discrete linearizability test based on multiscale analysis
• C-Integrability Test for Discrete Equations via Multiple Scale Expansions
• On the Integrability of the Discrete Nonlinear Schroedinger Equation
• Discrete Multiscale Analysis: A Biatomic Lattice System
• Multiscale expansion and integrability properties of the lattice potential KdV equation
• Continuous Symmetries of the Lattice Potential KdV Equation
• Multiscale reduction of discrete nonlinear Schroedinger equations