Bäcklund transformations for the isospectral and nonisospectral AKNS hierarchies

DOI10.1063/1.528617zbMath0726.58043OpenAlexW3087094564MaRDI QIDQ3350350

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Publication date: 1990

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528617

zbMATH Keywords

Bäcklund transformationsnonlinear evolution equationsLax pairsauto-Bäcklund transformationnonisospectral AKNS hierarchyisospectral AKNS hierarchyRiccati forms

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items

A generalized isospectral-nonisospectral heat equation hierarchy and its expanding integrable model ⋮ Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations ⋮ Darboux transformation for the non-isospectral AKNS hierarchy and its asymptotic property ⋮ Soliton-like solutions of three non-isospectral equations ⋮ Darboux transformation for the nonisospectral AKNS system ⋮ On the Treves theorem for the Ablowitz–Kaup–Newell–Segur equation ⋮ The Generalized Version of Dressing Method with Applications to AKNS Equations

Cites Work

• A unified explicit form of Bäcklund transformations for generalized hierarchies of KdV equations
• On the Bäcklund transformations for the generalized hierarchies of compound MKdV-SG equations
• On the Darboux matrices of Bäcklund transformations for AKNS systems
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Three kinds of Darboux transformation for the evolution equations which connect with A.K.N.S. eigenvalue problem