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Resonant scattering of solitons. (English) Zbl 1080.35538

Summary: We study the scattering of solitons in the nonlinear Schrödinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton’s velocity. The analytical predictions are tested numerically in regimes characterized by various time scales. Special attention is paid to intermode interactions and their effect on coherence, decoherence, and dephasing of plane-wave modes which build up the soliton.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35P25 Scattering theory for PDEs
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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