Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions

DOI10.1063/1.1388898zbMath1063.37065arXivnlin/0105061OpenAlexW3102264417MaRDI QIDQ2775037

Zi-Xiang Zhou, Wen-Xiu Ma

Publication date: 26 February 2002

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

Full work available at URL: https://arxiv.org/abs/nlin/0105061

Mathematics Subject Classification ID

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Cites Work

• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Do symmetry constraints nonlinearize spectral problems into Hamiltonian systems?
• Elementary and binary Darboux transformations at rings
• Separability and dynamical \(r\)-matrix for the constrained flows of the Jaulent-Miodek hierarchy
• On the complete integrability of nonlinearized Lax systems for the classical Boussinesq hierachy
• A finite-dimensional integrable system and the r-matrix method
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• On Liouville integrability of zero-curvature equations and the Yang hierarchy
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Integrable Hamiltonian systems related to the polynomial eigenvalue problem
• Restricted flows of the AKNS hierarchy
• How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Nonlinear constraints and soliton solutions of 1+2-dimensional three-wave equation
• Localized solitons of the hyperbolic su( N ) AKNS system
• On separability of bi-Hamiltonian chain with degenerated Poisson structures
• A finite-dimensional integrable system associated with the three-wave interaction equations
• Relation between the Kadometsev–Petviashvili equation and the confocal involutive system
• Integrable mechanical systems related to the Harry–Dym hierarchy
• New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
• Direct Construction of Conservation Laws from Field Equations
• Separation of variables for soliton equations via their binary constrained flows
• Linear r-matrix algebra for classical separable systems
• Integrals of nonlinear equations of evolution and solitary waves
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
• Three kinds of constraints of potential for KdV hierarchy

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