A finite-dimensional integrable system associated with the three-wave interaction equations

DOI10.1063/1.532896zbMath0955.37034OpenAlexW2062934425MaRDI QIDQ4270354

Yong-Tang Wu, Xiangguo Geng

Publication date: 21 November 1999

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

Full work available at URL: https://doi.org/10.1063/1.532896

zbMATH Keywords

soliton hierarchiesthree-wave interactionnonlinearization of inverse spectral problem

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (16)

Finite genus solutions of the generalized Merola–Ragnisco–Tu lattice hierarchy ⋮ Quasi-periodic solutions to the hierarchy of four-component Toda lattices ⋮ The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices ⋮ Adjoint Symmetry Constraints Leading to Binary Nonlinearization ⋮ Three-wave resonant interactions: multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics ⋮ Finite-dimensional integrable systems through the decomposition of a modified Boussinesq equation ⋮ New Neumann system associated with a \(3 \times 3\) matrix spectral problem ⋮ A finite-dimensional integrable system and the r-matrix method ⋮ Finite-band solutions for the hierarchy of coupled Toda lattices ⋮ Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions ⋮ A finite-dimensional integrable system related to a new coupled KdV hierarchy ⋮ Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions ⋮ Algebro-geometric integration of the modified Belov-Chaltikian lattice hierarchy ⋮ INTEGRABLE HAMILTONIAN SYSTEMS RELATED TO THE AKNS SYSTEM WITH MATRIX POTENTIALS ⋮ Algebro-geometric quasi-periodic solutions to the Bogoyavlensky lattice 2(3) equations ⋮ Three-sheeted Riemann surface and solutions of the Itoh–Narita–Bogoyavlensky lattice hierarchy

Cites Work

• The Hamiltonian structure and new finite-dimensional integrable system associated with Harry-Dym type equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Restricted flows of soliton hierarchies: coupled KdV and Harry Dym case
• Involutive solutions for toda and langmuir lattices through nonlinearization of lax pairs
• How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials
• Finite-dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem
• Miura map and Bi-Hamiltonian formulation for restricted flows of the KdV hierarchy
• On the relation of the stationary Toda equation and the symplectic maps
• A new integrable symplectic map associated with lattice soliton equations
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy

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