离散约化摄动法
Discrete Reductive Perturbation Technique
摘要：
本文将一个偏差分方程（P $Δ$ E）在多重晶格上展开，得到了控制其远场行为的P $Δ$ E。微扰-约化方法在这里进行众所周知的非线性P $Δ$ ES，可积和不可积。研究了格点修正的Korteweg-de Vries（mKdV）方程、Hietarinta方程、格点Volterra-Kac-Van Moerbeke（VKVM）方程和不可积格点KdV方程的情形.这样的减少使我们能够获得许多新的非线性薛定谔（NLS）型的P $Δ$ Es。
英文摘要：
We expand a partial difference equation (P$Δ$E) on multiple lattices and obtain the P$Δ$E which governs its far field behaviour. The perturbative--reductive approach is here performed on well known nonlinear P$Δ$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$Δ$Es of the nonlinear Schrödinger (NLS) type.
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