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Multipeakons of a two-component modified Camassa–Holm equation and the relation with the finite Kac–van Moerbeke lattice.

Authors :
Chang, Xiang-Ke
Hu, Xing-Biao
Szmigielski, Jacek
Source :
Advances in Mathematics. Aug2016, Vol. 299, p1-35. 35p.
Publication Year :
2016

Abstract

A spectral and the inverse spectral problem are studied for the two-component modified Camassa–Holm type for measures associated to interlacing peaks. It is shown that the spectral problem is equivalent to an inhomogeneous string problem with Dirichlet/Neumann boundary conditions. The inverse problem is solved by Stieltjes's continued fraction expansion, leading to an explicit construction of peakon solutions. Sufficient conditions for global existence of solutions are given. The large time asymptotics reveals that, asymptotically, peakons pair up to form bound states moving with constant speeds. The peakon flow is shown to project to one of the isospectral flows of the finite Kac–van Moerbeke lattice. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00018708
Volume :
299
Database :
Academic Search Index
Journal :
Advances in Mathematics
Publication Type :
Academic Journal
Accession number :
118151097
Full Text :
https://doi.org/10.1016/j.aim.2016.05.004