A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa–Holm system
DOI10.1088/1361-6544/abc101zbMath1464.35280arXiv2003.03114OpenAlexW3159092576MaRDI QIDQ4986214
Sondre Tesdal Galtung, Xavier Raynaud
Publication date: 27 April 2021
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.03114
calculus of variationsCamassa-Holm equationLagrangian coordinatestwo-component Camassa-Holm systemdiscrete Green's functionsdiscrete Sturm-Liouville operatorsenergy-preserving discretizations
KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Applications of difference equations (39A60) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80) Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K58)
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Cites Work
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- An energetic variational approach for ion transport
- Uniqueness of conservative solutions to the Camassa-Holm equation via characteristics
- Blow-up for the two-component Camassa-Holm system
- Parametric Poincaré-Perron theorem with applications
- The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
- On an integrable two-component Camassa-Holm shallow water system
- Convergence of products of matrices in projective spaces
- Dissipative solutions for the Camassa-Holm equation
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Global conservative solutions of the Camassa-Holm equation
- Well-posedness, blow-up phenomena and persistence properties for a two-component water wave system
- On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Functional analysis, Sobolev spaces and partial differential equations
- Wave breaking for nonlinear nonlocal shallow water equations
- Topological methods in hydrodynamics
- Geodesic flow on the diffeomorphism group of the circle
- Global weak solutions for a shallow water equation
- On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system
- Global conservative solutions to the Camassa-Holm equation for initial data with nonvanishing asymptotics
- On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
- Energetic variational approach in complex fluids: maximum dissipation principle
- A two-component generalization of the Camassa-Holm equation and its solutions
- Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
- Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics
- Least Action Principle for an Integrable Shallow Water Equation
- On a Camassa–Holm type equation with two dependent variables
- GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
- A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General $H^1$ Initial Data
- On the geometric approach to the motion of inertial mechanical systems
- An integrable shallow water equation with peaked solitons
- More on Poincaré’s and Perron’s Theorems for Difference Equations∗
- Global Solutions for the Two-Component Camassa–Holm System
- Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
- On hydrodynamics of viscoelastic fluids
- Convergence of a Finite Difference Scheme for the Camassa–Holm Equation
- Two-component equations modelling water waves with constant vorticity
