The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
2008/05/29 by Adrian Constantin, David Lannes · 48 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems
paper · doi:10.1007/s00205-008-0128-2
Citations
Cited by
- On the weakly dissipative Camassa–Holm, Degasperis–Procesi, and Novikov equations
- On the inconsistency of the Camassa-Holm model with the shallow water theory
- H "older Continuity of the Data to Solution Map for HR in the Weak\n Topology
- Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
- Quasi-confined modes produced by the Lugiato-Lefever model with a localized pump and the pseudo-Raman term
- Non-uniform dependence for the Novikov equation in Besov spaces
- Stability of peakons for the generalized modified Camassa-Holm equation
- Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces
- On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov\n equations
- Non-uniform dependence for higher dimensional Camassa-Holm equations in Besov spaces
- Darboux and Bäcklund transformations for the Camassa-Holm equation
- Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function
- The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem
- Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincaré equations
- The well-posedness, ill-posedness and non-uniform dependence on initial data for the Fornberg-Whitham equation in Besov spaces
- Non-uniform dependence for the two-component Camassa-Holm shallow water system
- On sharp global well-posedness and Ill-posedness for a fifth-order\n KdV-BBM type equation
- On the Cauchy problem for a two-component Degasperis-Procesi system
- Local well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude
- Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data
- On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
- Dynamical behavior near self-similar blowup waves for the generalized b-equation
- Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space
- On Isospectral flows related to (dual) cubic strings: Novikov, DP peakons and B, C-Toda lattices
- The Cauchy problem for the shallow water typ equations in low regularity spaces on the circle
- Stability of solitary waves of a generalized two-component Camassa-Holm system
- An integrable semi-discrete Degasperis-Procesi equation
- The Cauchy problem for the integrable RZQ equation
- Analysis on a generalized two-component Novikov system
- Existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation
- Asymptotic stability for some non positive perturbations of the Camassa-Holm peakon with application to the antipeakon-peakon profile
- On a Generalized System with Applications to Ideal Magnetohydrodynamics
- Liouville correspondences between multi-component integrable hierarchies
- The algebro-geometric solutions for the modified Camassa-Holm hierarchy
- The Burgers equation and the Korteweg-de Vries equation with quadratic nonlinearity
- Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems
- Well-Posedness of a kind of the free surface equation of shallow water wave
- On uniqueness of dissipative solutions of the Camassa-Holm equation
- Two-component CH system: inverse scattering, peakons and geometry
- The Camassa-Holm equation as an incompressible Euler equation: a\n geometric point of view
- Cauchy problem for a generalized cross-coupled Camassa-Holm system with waltzing peakons and higher-order nonlinearities
- Shock creation and Painlevé property of colliding peakons in the Degasperis-Procesi Equation
- Eigenvalues, bifurcation and one-sign solutions for the periodic p-Laplacian
- Orbital and asymptotic stability of a train of peakons for the Novikov equation
- The continuous dependence and non-uniform dependence of the rotation Camassa-Holm equation in Besov spaces
- Recent advances on the global regularity for irrotational water waves. [europepmc]
- Generalizations of the short pulse equation. [europepmc]
- Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics. [europepmc]