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