Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons

Y. A. Li; P. J. Olver

doi:10.3934/dcds.1997.3.419

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1997, Volume 3, Issue 3: 419-432. Doi: 10.3934/dcds.1997.3.419

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Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons

Y. A. Li^1, and
P. J. Olver^1,

1.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: August 31, 1996

Revised: December 31, 1996

Published: June 1997

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Abstract

We investigate how the non-analytic solitary wave solutions -- peakons and compactons -- of an integrable bi-Hamiltonian system arising in fluid mechanics, can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system. This phenomenon is examined to understand the important effect of linear dispersion terms on the analyticity of such homoclinic orbits.

Mathematics Subject Classification: 34A20, 34C35, 35B65, 58F05, 76B25.

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