Soliton surfaces and generalized symmetries of integrable systems

Abstract

In this paper, we discuss some specific features of symmetries of integrable systems which can be used to contruct the Fokas-Gel'fand formula for the immersion of 2D-soliton surfaces, associated with such systems, in Lie algebras. We establish the sufficient condition for the applicability of this formula. This condition requires the existence of two vector fields which generate a common symmetry of the initial system and its corresponding linear spectral problem. This means that these two fields have to be group-related and we determine an explicit form of this relation. It provides a criterion for the selection of symmetries suitable for the use of the Fokas-Gel'fand formula. We include some examples illustrating its application.

17 pages

References in corpus (4)

• Invariant recurrence relations for CP^(N-1) models
• On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model
• Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation
• Surfaces immersed in Lie algebras associated with elliptic integrals

Cited by in corpus (4)

• Classical-quantum correspondence for shape-invariant systems
• On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
• A cohomological approach to immersed submanifolds via integrable systems
• Liouville soliton surfaces obtained using Darboux transformations