On the Bäcklund transformation for the Gel'fand-Dickey equations

DOI10.1007/BF01941660zbMath0481.35075OpenAlexW2003442406MaRDI QIDQ1161868

Mark Adler

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1007/bf01941660

zbMATH Keywords

Bäcklund transformationToda equationsLax type equationsGel'fand-Dickey equations

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (13)

\(\tau\)-functions, Birkhoff factorizations and difference equations ⋮ Gauge theory of Bäcklund transformations. II ⋮ Group theoretical symmetries and generalized Bäcklund transformations for integrable systems ⋮ Darboux transformations for the \(\hat{A}_{2n}^{(2)}\)-KdV hierarchy ⋮ Central affine curve flow on the plane ⋮ Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows ⋮ On the Toda and KAC-VAN Moerbeke Systems ⋮ Factorization of random Jacobi operators and Bäcklund transformations ⋮ Specializations of integrable systems and affine Lie algebras ⋮ Darboux transforms for the \(\hat{B}_n^{(1)}\)-hierarchy ⋮ Bäcklund transformations for new fourth Painlevé hierarchies ⋮ A note on the generalized symmetries of lattice hierarchies ⋮ On the \(q\)-deformed modified Korteweg-de Vries hierarchy

Cites Work

• On a class of polynomials connected with the Korteweg-de Vries equation
• Linearization of Hamiltonian systems, Jacobi varieties and representation theory
• Modifying Lax equations and the second Hamiltonian structure
• The spectrum of difference operators and algebraic curves
• Three integrable Hamiltonian systems connected with isospectral deformations
• The spectrum of Jacobi matrices
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• On Some Periodic Toda Lattices
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

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