Invariant manifolds and separation of the variables for integrable chains

被引：3

作者：

Habibullin, I. T. ^{[1
,2
]}

Khakimova, A. R. ^{[1
]}

机构：

[1] Russian Acad Sci, Ufa Fed Res Ctr, Inst Math, 112 Chernyshevsky St, Ufa 450008, Russia

[2] Bashkir State Univ, 32 Validy St, Ufa 450076, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2020年 / 53卷 / 38期

关键词：

Volterra chain; explicit solutions; soliton; invariant manifold; LAX PAIRS; EQUATIONS;

D O I：

10.1088/1751-8121/aba399

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier, it has been observed that this kind of objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this article we show with an example of the Volterra chain that the generalized invariant manifold can be used for constructing exact particular solutions as well. To this end we first find an invariant manifold depending on two constant parameters. Then we assume that an ordinary difference equation (ODE) defining the generalized invariant manifold has a solution polynomially depending on one of the spectral parameters and derive an ODE, for the roots of the polynomials. The efficiency of the method is approved by some illustrative examples.

引用

页数：17