July  1997, 3(3): 419-432. doi: 10.3934/dcds.1997.3.419

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

1. 

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States, United States

Received  September 1996 Revised  January 1997 Published  April 1997

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.
Citation: Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 419-432. doi: 10.3934/dcds.1997.3.419
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