Solving AKNS equations via Jacobi inversion problem

DOI10.1007/BF02684033zbMath1010.37038OpenAlexW129595073MaRDI QIDQ1864214

Yunbo Zeng

Publication date: 17 March 2003

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02684033

zbMATH Keywords

factorizationHamiltonian systemLax representationsoliton equationsseparation of variables

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Cites Work

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• Nonlinearization of the Lax system for AKNS hierarchy
• A unified approach to Painlevé expansions
• New factorization of the Kaup-Newell hierarchy
• Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables
• Separability and dynamical \(r\)-matrix for the constrained flows of the Jaulent-Miodek hierarchy
• RESTRICTED FLOWS OF THE KdV HIERARCHY AND r-MATRIX FORMALISM
• Theta functions and non-linear equations
• Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet
• The deduction of the Lax representation for constrained flows from the adjoint representation
• A family of separable integrable Hamiltonian systems and their classical dynamical r -matrix Poisson structures
• The Lax representation and Darboux transformation for constrained flows of the AKNS hierarchy

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