scientific article; zbMATH DE number 5044695

zbMath1102.35006arXivmath-ph/0404016MaRDI QIDQ5481337

Yarema A. Prykarpatsky, Anatoliy K. Prykarpatsky, Jolanta Golenia, A. M. Samoilenko

Publication date: 9 August 2006

Full work available at URL: https://arxiv.org/abs/math-ph/0404016

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zbMATH Keywords

Darboux transformationsinverse spectral transformZakharov-Shabat equationspolynomial operator pencils

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Linear higher-order PDEs (35G05) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (7)

Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization ⋮ The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension ⋮ The spectral and differential geometric aspects of a generalized De Rham--Hodge theory related with Delsarte transmutation operators in multidimension and its applications to spectral and soliton problems ⋮ Theory of multidimensional Delsarte-Lions transmutation operators. II ⋮ Theory of multidimensional Delsarte-Lions transmutation operators. I ⋮ On the Bäcklund transformations of the Riccati equation: the differential-geometric approach revisited ⋮ On de Rham-Hodge-Skrypnik theory of Delsarte transmutation operators in multidimension and its applications

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