Integrable nonlinear field equations and loop algebra structures

Abstract

We apply the (direct and inverse) prolongation method to a couple of nonlinear Schr{ö}dinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a procedure with allows us to generate a new class of integrable nonlinear field equations containing the original ones as a special case.

13 pages, latex, no figures,

References in corpus (1)

• Algebraic properties of the 1+1 dimensional Heisenberg spin field model

Cited by in corpus (4)

• Generalized Sum Rules for Spin-Dependent Structure Functions of the Nucleon
• Nonlinear 2+1--Dimensional Field Equations from Incomplete Lie Algebra Structures
• Bäcklund loop algebras for compact and non-compact nonlinear spin models in $(2+1)$ dimensions
• Constructing towers with skeletons from open Lie algebras and integrability