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

Abstract

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