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