The string density problem and the Camassa–Holm equation

DOI10.1098/rsta.2007.2010zbMath1152.35468OpenAlexW2120389126WikidataQ36759775 ScholiaQ36759775MaRDI QIDQ5301948

David H. Sattinger, Richard W. Beals, Jacek Szmigielski

Publication date: 20 January 2009

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rsta.2007.2010

zbMATH Keywords

Camassa-Holm equationspectral problemmulti-peakonstring density problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30)

Related Items (10)

An Inverse Spectral Problem Related to the Geng–Xue Two-Component Peakon Equation ⋮ The inverse spectral problem for indefinite strings ⋮ Isospectral flows for the inhomogeneous string density problem ⋮ The string of variable density: perturbative and non-perturbative results ⋮ Unique solvability of a coupling problem for entire functions ⋮ Long time asymptotics of the Camassa-Holm equation on the half-line ⋮ On isospectral deformations of an inhomogeneous string ⋮ Integrable generalization of the associated Camassa-Holm equation ⋮ STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS ⋮ Information Geometry and Integrable Hamiltonian Systems

Cites Work

• On the scattering problem for the Camassa-Holm equation
• On the spectral functions of the string
• An integrable shallow water equation with peaked solitons

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