Convergence of Solitary-wave Solutions in a Perturbed Bi-hamiltonian Dynamical System. I. Compactons and Peakons

We investigate how the non-analytic solitary wave solutions — peakons and compactons — of an integrable biHamiltonian 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.