Riemann-Hilbert approach for the Camassa-Holm equation on the line
From MaRDI portal
Publication:869459
DOI10.1016/j.crma.2006.10.014zbMath1110.35056OpenAlexW2167128723MaRDI QIDQ869459
Anne Boutet de Monvel-Berthier, Dimitry Shepelsky
Publication date: 2 March 2007
Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.crma.2006.10.014
Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Riemann-Hilbert problems in context of PDEs (35Q15)
Related Items (52)
Persistence properties for the Fokas-Olver-Rosenau-Qiao equation in weighted \(L^{p}\) spaces ⋮ On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions ⋮ The global attractor for a viscous weakly dissipative generalized two-component \(\mu\)-Hunter-Saxton system ⋮ Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial data ⋮ A Riemann-Hilbert approach for the Novikov equation ⋮ The Cauchy problem for a generalized Dullin–Gottwald–Holm equation in Besov spaces ⋮ Long-time asymptotics for the modified complex short pulse equation ⋮ Soliton resolution for the short-pulse equation ⋮ Riemann-Hilbert approach and long-time asymptotics of the positive flow short-pulse equation ⋮ The short pulse equation by a Riemann-Hilbert approach ⋮ Well-posedness, blow-up phenomena and global existence for the generalized \(b\)-equation with higher-order nonlinearities and weak dissipation ⋮ Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations ⋮ Inverse scattering transform for the complex coupled short‐pulse equation ⋮ On the asymptotic stability of \(N\)-soliton solution for the short pulse equation with weighted Sobolev initial data ⋮ Lump, breather and interaction solutions to the (3+1)-dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation ⋮ The Cauchy problem of the Camassa-Holm equation in a weighted Sobolev space: long-time and Painlevé asymptotics ⋮ A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions ⋮ Lipschitz metric for the modified coupled Camassa–Holm system ⋮ A new 3-component Degasperis-Procesi hierarchy ⋮ Multiple higher-order pole solutions of modified complex short pulse equation ⋮ Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data ⋮ Soliton resolution for the complex short-pulse positive flow with weighted Sobolev initial data in the space-time soliton regions ⋮ Long-time asymptotics of the Hunter-Saxton equation on the line ⋮ Dressing Method for the Degasperis-Procesi Equation ⋮ Well-posedness and blow-up phenomena for a higher order shallow water equation ⋮ A Riemann–Hilbert approach for the modified short pulse equation ⋮ Global conservative solutions for a modified periodic coupled Camassa-Holm system ⋮ Local well-posedness and persistence properties for a model containing both Camassa-Holm and Novikov equation ⋮ The Cauchy problem for a generalized \(b\)-equation with higher-order nonlinearities in critical Besov spaces and weighted \(L^p\) spaces ⋮ Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions ⋮ The Camassa-Holm equation on the half-line: a Riemann-Hilbert approach ⋮ Continuity and analyticity for a cross-coupled Camassa-Holm equation with waltzing peakons and compacton pairs ⋮ The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data ⋮ Bäcklund transformations for the Camassa-Holm equation ⋮ Long time asymptotics of the Camassa-Holm equation on the half-line ⋮ Cuspons and smooth solitons of the Degasperis-Procesi equation under inhomogeneous boundary condition ⋮ Optimal control of the viscous generalized Camassa-Holm equation ⋮ The Camassa-Holm equation on the half-line with linearizable boundary condition ⋮ The global attractor of the viscous Fornberg-Whitham equation ⋮ The attractor of a parabolic-elliptic system ⋮ Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions ⋮ Camassa-Holm cuspons, solitons and their interactions via the dressing method ⋮ Solving the modified complex short pulse equation of focusing type: a Riemann-Hilbert approach ⋮ Time-periodic solution of the weakly dissipative Camassa-Holm equation ⋮ Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations ⋮ Long time behavior and soliton solution for the Harry Dym equation ⋮ A view of the peakon world through the lens of approximation theory ⋮ Optimal control of the viscous weakly dispersive Degasperis-Procesi equation ⋮ Optimal solution for the viscous nonlinear dispersive wave equation ⋮ On the soliton resolution and the asymptotic stability of \(N\)-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions ⋮ Uniqueness and stability of global conservative solutions for the modified coupled Camassa–Holm system ⋮ The local well-posedness, existence and uniqueness of weak solutions for a model equation for shallow water waves of moderate amplitude
Cites Work
- Unnamed Item
- A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
- On the scattering problem for the Camassa-Holm equation
- On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves
- Inverse scattering transform for the Camassa–Holm equation
- Multi-peakons and a theorem of Stieltjes
- A shallow water equation on the circle
- Fredholm determinants and the Camassa-Holm hierarchy
- Stability of peakons
- An integrable shallow water equation with peaked solitons
- Parametric Representation for the Multisoliton Solution of the Camassa–Holm Equation
This page was built for publication: Riemann-Hilbert approach for the Camassa-Holm equation on the line
