Long-time Asymptotics for the Camassa–Holm Equation

From MaRDI portal
Publication:3584126

DOI10.1137/090748500zbMath1204.37073arXiv0902.0391OpenAlexW1992838303WikidataQ56564070 ScholiaQ56564070MaRDI QIDQ3584126

Gerald Teschl, Dimitry Shepelsky, Aleksey S. Kostenko, Anne Boutet de Monvel-Berthier

Publication date: 19 August 2010

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.0391




Related Items (only showing first 100 items - show all)

Orbital stability of solitary traveling waves of moderate amplitudeBlow-up of solutions for the dissipative Dullin-Gottwald-Holm equation with arbitrary coefficientsLocal well-posedness and blow-up for a family of \(U(1)\)-invariant peakon equationsTHE RIEMANN–HILBERT APPROACH TO OBTAIN CRITICAL ASYMPTOTICS FOR HAMILTONIAN PERTURBATIONS OF HYPERBOLIC AND ELLIPTIC SYSTEMSLong-time asymptotics for the generalized Sasa-Satsuma equationOn the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regionsRiemann-Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equationLong time and Painlevé-type asymptotics for the Sasa-Satsuma equation in solitonic space time regionsA nonlocal shallow-water model arising from the full water waves with the Coriolis effectThe Cauchy problem and wave-breaking phenomenon for a generalized sine-type FORQ/mCH equationA Riemann-Hilbert approach for the Novikov equationAsymptotics of step-like solutions for the Camassa-Holm equationDevelopment of a numerical phase optimized upwinding combined compact difference scheme for solving the Camassa-Holm equation with different initial solitary wavesLong-time asymptotics for the short pulse equationLong-time asymptotics for the modified complex short pulse equationStability of periodic peaked solitary waves for a cubic Camassa-Holm-type equationSoliton resolution for the short-pulse equationRiemann-Hilbert approach and long-time asymptotics of the positive flow short-pulse equationDefocusing NLS equation with nonzero background: large-time asymptotics in a solitonless regionThe short pulse equation by a Riemann-Hilbert approachBlow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equationLong-time asymptotics for the spin-1 Gross-Pitaevskii equationLong-time asymptotic behavior for the discrete defocusing mKdV equationThe Riemann-Hilbert problem and long-time asymptotics for the Kundu-Eckhaus equation with decaying initial valueOn a shallow water equation perturbed in Schwartz classLong-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial dataOrbital stability of solitary waves of moderate amplitude in shallow waterLong-time asymptotics of a three-component coupled nonlinear Schrödinger system\(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systemsLong-time asymptotics for the Degasperis-Procesi equation on the half-lineExistence of the periodic peaked solitary-wave solutions to the Camassa-Holm-Kadomtsev-Petviashvili equationLong-time asymptotics of the coupled modified Korteweg-de Vries equationAsymptotic expansions and solitons of the Camassa-Holm - nonlinear Schrödinger equationLong time asymptotic behavior for the nonlocal mKdV equation in solitonic space-time regionsOn the initial value problem for the two-coupled Camassa-Holm system in Besov spacesGeneric regularity of conservative solutions to the rotational Camassa-Holm equationPersistence properties and unique continuation of solutions to a two-component Camassa-Holm equationLong-time asymptotic behavior for the complex short pulse equationSpectral analysis and long-time asymptotics for the Harry Dym-type equation with the Schwartz initial dataWave-breaking and peakons for a modified Camassa-Holm equationA Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditionsOne-dimensional weakly nonlinear model equations for Rossby wavesLocal well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitudeGlobal weak solutions for a generalized Novikov equationGlobal weak solutions for a two-component Camassa–Holm system with an arbitrary smooth functionTraveling surface waves of moderate amplitude in shallow waterThe Ostrovsky-Vakhnenko equation: A Riemann-Hilbert approachOn the behavior of the solution of the dissipative Camassa-Holm equation with the arbitrary dispersion coefficientRiemann-Hilbert method for the Wadati-Konno-Ichikawa equation: \(N\) simple poles and one higher-order poleOn the low regularity solutions and wave breaking for an equation modeling shallow water waves of moderate amplitudeBlow-up phenomena and peakons for the \(b\)-family of FORQ/MCH equationsNumerical study of long-time Camassa-Holm solution behavior for soliton transportA note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearityNon-uniform dependence on initial data for the periodic Constantin-Lannes equationLong-time asymptotic behavior for a fourth-order dispersive nonlinear Schrödinger equationThe nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equationThe Cauchy problem for a generalized Novikov equationLong-time asymptotics of solutions for the coupled dispersive AB system with initial value problemsOn blow-up criteria for a class of nonlinear dispersive wave equations with dissipationLong time asymptotics of the Camassa-Holm equation on the half-lineInitial-boundary value problem for the Camassa-Holm equation with linearizable boundary conditionOn the small-amplitude long waves in linear shear flows and the Camassa-Holm equationThe rotational speed limit and the blow-up phenomena of the rotation 2-component Camassa-Holm systemA necessary and sufficient condition for the solvability of the nonlinear Schrödinger equation on a finite intervalThe Camassa-Holm equation on the half-line with linearizable boundary conditionThe Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equationLocal-in-space blow-up criteria for a class of nonlinear dispersive wave equationsOptimal control of a class of nonlocal dispersive equationsSpectral analysis and long-time asymptotics for the potential Wadati-Konno-Ichikawa equationNon-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torusNon-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitudeThe local well-posedness in Besov spaces and non-uniform dependence on initial data for the interacting system of Camassa-Holm and Degasperis-Procesi equationsOn the persistence and blow up for the generalized two-component Dullin-Gottwald-Holm systemLong-time asymptotics for the focusing Hirota equation with non-zero boundary conditions at infinity via the Deift-Zhou approachSmooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equationsSymmetric waves are traveling waves for the rotation-Camassa-Holm equationLong-Time Asymptotics for the Nonlocal MKdV Equation*Long-time asymptotics for the focusing Fokas-Lenells equation in the solitonic region of space-timePersistence properties for the two-component Novikov equation in weighted Lp spacesBi-Hamiltonian Structure of a Three-Component Camassa-Holm Type EquationOn a spectral analysis of scattering data for the Camassa-Holm equationLong-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering dataOrbital stability of solitary waves and a Liouville-type property to the cubic Camassa-Holm-type equationLong time behavior and soliton solution for the Harry Dym equationSpectral analysis and long-time asymptotics of a coupled nonlinear Schrödinger systemLong time asymptotics for the nonlocal mKdV equation with finite density initial dataA sine-type Camassa-Holm equation: local well-posedness, Hölder continuity, and wave-breaking analysisThe periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm systemApplication of the nonlinear steepest descent method to the general coupled nonlinear Schrödinger systemWave breaking and solitary wave solutions for a generalized Novikov equationLong-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitonsNonuniform dependence for the Cauchy problem of the general b-equationRiemann-Hilbert problem for Camassa-Holm equation with step-like initial dataLong-time asymptotic behavior for the derivative Schrödinger equation with finite density type initial dataThe global weak solutions to the Cauchy problem of the generalized Novikov equationSpectral analysis and long-time asymptotics for the coherently-coupled nonlinear Schrödinger systemOn the wave length of smooth periodic traveling waves of the Camassa-Holm equationQuadratic operator pencils associated with the conservative Camassa-Holm flowAsymptotics in shallow water wavesBlow-up phenomena and global existence for a two-component Camassa-Holm system with an arbitrary smooth function




This page was built for publication: Long-time Asymptotics for the Camassa–Holm Equation