Li, Y. A.; Olver, P. J. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons. (English) Zbl 0949.35118 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. Cited in 1 ReviewCited in 51 Documents 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 PDF BibTeX XML Cite \textit{Y. A. Li} and \textit{P. J. Olver}, Discrete Contin. Dyn. Syst. 3, No. 3, 419--432 (1997; Zbl 0949.35118) Full Text: DOI OpenURL