Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV

Abstract

We consider multiple lattices and functions defined on them. We introduce slow varying conditions for functions defined on the lattice and express the variation of a function in terms of an asymptotic expansion with respect to the slow varying lattices. We use these results to perform the multiple--scale reduction of the lattice potential Korteweg--de Vries equation.

17 pages. 1 figure

References in corpus (2)

• A new two-dimensional lattice model that is "consistent around a cube"
• Singularity analysis of a new discrete nonlinear Schrodinger equation

Cited by in corpus (8)

• Discrete Reductive Perturbation Technique
• A discrete linearizability test based on multiscale analysis
• On the Integrability of the Discrete Nonlinear Schroedinger Equation
• C-Integrability Test for Discrete Equations via Multiple Scale Expansions
• Multiscale expansion and integrability properties of the lattice potential KdV equation
• Integrability of Differential-Difference Equations with Discrete Kinks
• Multiscale reduction of discrete nonlinear Schroedinger equations
• Continuous Symmetries of the Lattice Potential KdV Equation