Colliding solitons for the nonlinear Schrodinger equation

Abstract

We study the collision of two fast solitons for the nonlinear Schrödinger equation in the presence of a spatially adiabatic external potential. For a high initial relative speed $\Vert v\Vert$ of the solitons, we show that, up to times of order $\log \Vert v\Vert$ after the collision, the solitons preserve their shape (in $L^2$-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.

27 pages

References in corpus (3)

• Solitary Wave Dynamics in an External Potential
• Fast soliton scattering by delta impurities
• Solitary wave dynamics in time-dependent potentials

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• Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with the same mass
• Interaction of coherent states for Hartree equations