New Lax pair for restricted multiple three wave interaction system, quasiperiodic solutions and bi-Hamiltonian structure

DOI10.1134/S1560354708060099zbMath1229.37094arXiv0705.4363MaRDI QIDQ652998

Andreĭ Vladimirovich Tsyganov, Nikolay A. Kostov

Publication date: 6 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.4363

zbMATH Keywords

bi-Hamiltonian structureLax pairthree wave interaction system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Perturbation methods for rigid body dynamics (70E20)

Related Items (3)

Second order Killing tensors related to symmetric spaces ⋮ The Poisson bracket compatible with the classical reflection equation algebra ⋮ Finite‐Dimensional Integrable Hamiltonian Systems Related to the Nonlinear Schrödinger Equation

Cites Work

• Unnamed Item
• Restricted multiple three-wave interactions: Integrable cases of this system and other related systems
• Coupling of surface and internal gravity waves: a mode coupling model
• On two different bi-Hamiltonian structures for the Toda lattice
• A family of the Poisson brackets compatible with the Sklyanin bracket

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