An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation

DOI10.1007/s00220-014-1905-4zbMath1297.35204arXiv1406.3702OpenAlexW1995258415WikidataQ62469505 ScholiaQ62469505MaRDI QIDQ2249770

Jonathan Eckhardt, Aleksey S. Kostenko

Publication date: 3 July 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.3702

zbMATH Keywords

integrabilityshallow-water waveswave collapsepeakonsconservative solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton equations (35Q51)

Related Items (29)

The inverse spectral problem for indefinite strings ⋮ Hermite-Padé approximations with Pfaffian structures: Novikov peakon equation and integrable lattices ⋮ The classical moment problem and generalized indefinite strings ⋮ Minimization of lowest positive periodic eigenvalue for the Camassa–Holm equation with indefinite potential ⋮ Moment modification, multipeakons, and nonisospectral generalizations ⋮ Geometric singular perturbation analysis to Camassa-Holm Kuramoto-Sivashinsky equation ⋮ A numerical study of variational discretizations of the Camassa-Holm equation ⋮ Stumpons are non-conservative traveling waves of the Camassa-Holm equation ⋮ Continuous dependence and estimates of eigenvalues for periodic generalized Camassa-Holm equations ⋮ Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy ⋮ Trace of order \((-1)\) for a string with singular weight ⋮ Criterion for Lyapunov stability of periodic Camassa-Holm equations ⋮ On the isospectral problem of the Camassa-Holm equation ⋮ Continued fraction expansions of Herglotz–Nevanlinna functions and generalized indefinite strings of Stieltjes type ⋮ Sharp bounds for Dirichlet eigenvalue ratios of the Camassa-Holm equations ⋮ Spectral asymptotics for canonical systems ⋮ Traces of higher negative orders for a string with a singular weight ⋮ The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data ⋮ Unique solvability of a coupling problem for entire functions ⋮ Trace formulas and continuous dependence of spectra for the periodic conservative Camassa-Holm flow ⋮ On the absolutely continuous spectrum of generalized indefinite strings ⋮ Instability of \(H^1\)-stable peakons in the Camassa-Holm equation ⋮ Refining eigenvalue estimates for a string with a singular weight ⋮ Growth of Perturbations to the Peaked Periodic Waves in the Camassa--Holm Equation ⋮ A view of the peakon world through the lens of approximation theory ⋮ On the absolutely continuous spectrum of generalized indefinite strings. II ⋮ Continuity and minimization of spectrum related with the periodic Camassa-Holm equation ⋮ Relatively bounded perturbations of \(J\)-non-negative operators ⋮ Quadratic operator pencils associated with the conservative Camassa-Holm flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sturm-Liouville operators with measure-valued coefficients
• Scattering and inverse scattering for a left-definite Sturm-Liouville problem
• 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
• A convergent numerical scheme for the Camassa-Holm equation based on multipeakons
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Acoustic scattering and the extended Korteweg-de Vries hierarchy
• Wave breaking for nonlinear nonlocal shallow water equations
• Direct and inverse spectral problems for generalized strings
• Global weak solutions for a shallow water equation
• Multipeakons and the classical moment problem
• On the isospectral problem of the dispersionless Camassa-Holm equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• On the weak solutions to a shallow water equation
• On the scattering problem for the Camassa-Holm equation
• Structured Matrices, Continued Fractions, and Root Localization of Polynomials
• On Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces
• Inverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm–Liouville Problem
• Inverse scattering transform for the Camassa–Holm equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• GLOBAL CONSERVATIVE MULTIPEAKON SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Global Dissipative Multipeakon Solutions of the Camassa–Holm Equation
• Variational derivation of the Camassa-Holm shallow water equation
• On the spectral functions of the string
• Fredholm determinants and the Camassa-Holm hierarchy
• Breakdown of the Camassa-Holm equation
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination

This page was built for publication: An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation