Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons. (English) Zbl 0949.35118

Li, Y. A.; Olver, P. J.

Discrete Contin. Dyn. Syst. 3, No. 3, 419-432 (1997).

Summary: 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.

MSC:

35Q51	Soliton equations
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
76B25	Solitary waves for incompressible inviscid fluids
35Q58	Other completely integrable PDE (MSC2000)

Keywords:

non-analytic solitary wave solutions; integrable bi-Hamiltonian system; limits of classical solitary wave solutions