Discrete Reductive Perturbation Technique

Details Discrete Reductive Perturbation Technique Discrete Reductive Perturbation Technique

2005-10-25

arxiv.org/abs/math-ph/0510084v1

Physics

Mathematical Physics

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

Scientific paper

10.1063/1.2190776

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 Schr\"odinger (NLS) type.

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