Integrable hierarchy, \(3\times 3\) constrained systems, and parametric solutions

DOI10.1023/B:ACAP.0000038872.88367.ddzbMath1078.37045OpenAlexW1983234399MaRDI QIDQ702058

Zhijun Qiao

Publication date: 17 January 2005

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:acap.0000038872.88367.dd

zbMATH Keywords

integrabilitynonlinear evolution equationsfinite-dimensional Hamiltonian systemszero curvature representation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (24)

On generating linear and nonlinear integrable systems with variable coefficients ⋮ An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation ⋮ An integrable equation with nonsmooth solitons ⋮ Global existence and propagation speed for a generalized Camassa-Holm model with both dissipation and dispersion ⋮ Globally conservative weak solutions for a class of nonlinear dispersive wave equations beyond wave breaking ⋮ M-shape peakons, dehisced solitons, cuspons and new 1-peak solitons for the Degasperis-Procesi equation ⋮ MULTI-PEAKON SOLUTIONS TO A FOUR-COMPONENT CAMASSA-HOLM TYPE SYSTEM ⋮ Blow-up phenomena and peakons for the \(b\)-family of FORQ/MCH equations ⋮ Cusp and loop soliton solutions of short-wave models for the Camassa-Holm and Degasperis-Procesi equations ⋮ A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy ⋮ Conserved quantities, global existence and blow-up for a generalized CH equation ⋮ Cuspons and smooth solitons of the Degasperis-Procesi equation under inhomogeneous boundary condition ⋮ Decomposition method for the Camassa-Holm equation ⋮ A new super-extension of the KdV hierarchy ⋮ Application of variational iteration method for modified Camassa‐Holm and Degasperis‐Procesi equations ⋮ Qualitative analysis for a new integrable two-component Camassa-Holm system with peakon and weak kink solutions ⋮ Algebro-geometric solutions for the derivative Burgers hierarchy ⋮ On a new two-component \(b\)-family peakon system with cubic nonlinearity ⋮ A new integrable symplectic map for 4-field Blaszak-Marciniak lattice equations ⋮ The Application of Neumann Type Systems for Solving Integrable Nonlinear Evolution Equations ⋮ Global existence and long time behavior of the generalized Camassa–Holm equation with k + 1 degree nonlinearities ⋮ A super-discrete variational identity and its application for constructing super-discrete Hamiltonian systems ⋮ A view of the peakon world through the lens of approximation theory ⋮ Coupling integrable couplings and bi-Hamiltonian structure associated with the Boiti–Pempinelli–Tu hierarchy

Cites Work

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• Nonlinearization of the Lax system for AKNS hierarchy
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
• The Camassa-Holm hierarchy, \(N\)-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold
• On billiard solutions of nonlinear PDEs
• Cusp Soliton of a New Integrable Nonlinear Evolution Equation
• Nonlinear-Evolution Equations of Physical Significance
• Method for Solving the Korteweg-deVries Equation
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A shallow water equation on the circle
• GENERALIZED r-MATRIX STRUCTURE AND ALGEBRO-GEOMETRIC SOLUTION FOR INTEGRABLE SYSTEM
• An integrable shallow water equation with peaked solitons
• On the link between umbilic geodesics and soliton solutions of nonlinear PDEs
• An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems
• The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type

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