The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy

DOI10.1007/BF02108164zbMath0867.35088OpenAlexW178300579MaRDI QIDQ4897057

Yunbo Zeng, Yi-Shen Li

Publication date: 4 August 1997

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

Full work available at URL: https://doi.org/10.1007/bf02108164

zbMATH Keywords

Lax representationDarboux transformationadjoint representationconstrained flow

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items

Integrability of a differential-difference KP equation with self-consistent sources ⋮ 2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Bäcklund transformation and Lax pair ⋮ Integrability of the semi-discrete Toda equation with self-consistent sources ⋮ The Painlevé tests, Bäcklund transformation and bilinear form for the KdV equation with a self-consistent source ⋮ The \(N\)-soliton solutions of some soliton equations with self-consistent sources ⋮ Integration of the soliton hierarchy with self-consistent sources ⋮ On an integrable two-dimensional special lattice with self-consistent sources ⋮ On the extended KdV equation with self-consistent sources ⋮ The negative extended KdV equation with self-consistent sources: soliton, positon and negaton ⋮ Solving the KdV hierarchy with self-consistent sources by inverse scattering method ⋮ Two kinds of new integrable decompositions of the Gerdjikov-Ivanov equation ⋮ Solving AKNS equations via Jacobi inversion problem ⋮ The \(N\)-soliton solutions of the sine-Gordon equation with self-consistent sources ⋮ A family of integrable systems of Liouville and Lax representation, Darboux transformations for its constrained flows

Cites Work

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• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• On the Darboux matrices of Bäcklund transformations for AKNS systems
• An approach to the integrability of Hamiltonian systems obtained by reduction
• The constraints of potentials and the finite-dimensional integrable systems
• Three kinds of Darboux transformation for the evolution equations which connect with A.K.N.S. eigenvalue problem
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The deduction of the Lax representation for constrained flows from the adjoint representation

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