Three kinds of Darboux transformation for the evolution equations which connect with A.K.N.S. eigenvalue problem

DOI10.1007/BF02565027zbMath0669.35098MaRDI QIDQ3822618

Xinshen Gu, Maorong Zou, Yi-Shen Li

Publication date: 1987

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

zbMATH Keywords

evolution equationsDarboux transformationhierarchyA.K.N.S. eigenvalue problem

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (18)

Darboux transformations and soliton-like solutions of a new system associated with the negative AKNS system ⋮ N-fold Darboux Transformation for Integrable Couplings of AKNS Equations ⋮ A correspondence between AKNS hierarchy and the JM hierarchy ⋮ Determinant representation of Darboux transformation for the AKNS system ⋮ Explicit solutions of some (2+1)-dimensional differential-difference equations ⋮ The \(n\)-fold Darboux transformation for the Kundu-Eckhaus equation and dynamics of the smooth positon solutions ⋮ Bidirectional soliton solutions of the classical Boussinesq system and AKNS system. ⋮ Explicit \(N\)-fold Darboux transformation for the classical Boussinesq system and multi-soliton solutions ⋮ The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy ⋮ A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures ⋮ Double Darboux Transformation for AKNS hierarchy ⋮ Bäcklund transformations for the isospectral and nonisospectral AKNS hierarchies ⋮ A few integrable systems and spatial spectral transformations ⋮ Riemann-Hilbert approach and \(N\)-soliton solutions of the generalized mixed nonlinear Schrödinger equation with nonzero boundary conditions ⋮ Darboux transformations of the Supersymmetric BKP hierarchy ⋮ The determinant representation of an N-fold Darboux transformation for the short pulse equation ⋮ Darboux transformation of the second-type derivative nonlinear Schrödinger equation ⋮ Integrable discretizations for classical Boussinesq system

Cites Work

• Darboux transformations associated with Boiti-Tu eigenvalue problem

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