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Scattering for a particle interacting with a Bose gas. (English) Zbl 1462.35359

Summary: We study the long-time behavior of solutions to an ODE-Schrödinger type system that models the interaction of a particle with a Bose gas. We show that the particle has sonic or subsonic ballistic trajectory asymptotically, and that the wave function describing the Bose gas converges to a soliton in \(L^\infty\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
82D05 Statistical mechanics of gases
35C08 Soliton solutions
76G25 General aerodynamics and subsonic flows
35B40 Asymptotic behavior of solutions to PDEs
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