Fast Soliton Scattering by Delta Impurities

By Justin Holmer, Jeremy Louis Marzuola, Maciej Zworski. 2006

148 citations recorded by the source corpus.

We study the Gross-Pitaevskii equation with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/428c58447271ea4fd482afcae549e6e13cf2e227

Citations in the corpus

• Why are solitons stable (2008, unknown): “Somewhat similar in spirit, there has been some recent work in [27], [26] investigating the collision between a fast soliton and a localised potential (such as a delta function potential).”