Liouville correspondences between multicomponent integrable hierarchies
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Publication:2193749
DOI10.1134/S0040577920070028zbMath1457.37087arXiv1805.01665OpenAlexW3043773931MaRDI QIDQ2193749
Jing Kang, Peter J. Olver, Xiao-Chuan Liu, Chang-Zheng Qu
Publication date: 20 August 2020
Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.01665
bi-Hamiltonian structureLiouville transformationtwo-component Camassa-Holm systemtwo-component Novikov systemtwo-component dual dispersive water wave system
PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)
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A view of the peakon world through the lens of approximation theory, Reciprocal transformations of generalized negative flows in integrable hierarchies
Cites Work
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- Multi-component integrable systems and invariant curve flows in certain geometries
- On bi-Hamiltonian structure of two-component Novikov equation
- Oscillation-induced blow-up to the modified Camassa-Holm equation with linear dispersion
- The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
- On an integrable two-component Camassa-Holm shallow water system
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems
- On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Coupled KdV equations with multi-Hamiltonian structures
- Darboux' theorem for Hamiltonian differential operators
- Liouville transformation and exactly solvable Schrödinger equations
- Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
- Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
- Wave-breaking and peakons for a modified Camassa-Holm equation
- A new Liouville transformation for the Geng-Xue system
- A two-component generalization of the Camassa-Holm equation and its solutions
- Orbital stability of the train of peakons for an integrable modified Camassa-Holm equation
- Geodesic flow and two (super) component analog of the Camassa-Holm equation
- Mathematics of dispersive water waves
- Liouville correspondences between integrable hierarchies
- A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
- A Higher-Order Water-Wave Equation and the Method for Solving It
- A Synthetical Two-Component Model with Peakon Solutions
- Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations
- Two-component generalizations of the Camassa–Holm equation
- Two-component CH system: inverse scattering, peakons and geometry
- An extension of integrable peakon equations with cubic nonlinearity
- Hodograph Transformations of Linearizable Partial Differential Equations
- Integrable peakon equations with cubic nonlinearity
- Generalizations of the Camassa–Holm equation
- Coupled Harry Dym equations with multi-Hamiltonian structures
- The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants
- Approximate equations for long water waves
- A new hierarchy of Korteweg–de Vries equations
- Evolution equations possessing infinitely many symmetries
- A simple model of the integrable Hamiltonian equation
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- The Liouville correspondence between the Korteweg—de Vries and the Camassa‐Holm hierarchies
- An integrable shallow water equation with peaked solitons
- Traveling Wave Solutions of the Camassa-Holm and Korteweg-de Vries Equations
- The correspondence between KdV and Camassa-Holm
- A Lagrangian View on Complete Integrability of the Two-Component Camassa–Holm System
- Dynamics of interlacing peakons (and shockpeakons) in the Geng–Xue equation
- Bäcklund transformations for tri-Hamiltonian dual structures of multi-component integrable systems
- Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
- Prolongation algebras and Hamiltonian operators for peakon equations
- On the blow-up of solutions to the integrable modified Camassa–Holm equation
- A reciprocal transformation for the Geng-Xue equation
- An Inverse Spectral Problem Related to the Geng–Xue Two-Component Peakon Equation
- Multisoliton solutions of the two-component Camassa–Holm system and their reductions
- Bäcklund transformation and smooth multisoliton solutions for a modified Camassa-Holm equation with cubic nonlinearity
- Integrals of nonlinear equations of evolution and solitary waves
- Integrable Models for Shallow Water with Energy Dependent Spectral Problems
- Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy
