TRANSMISSION OF FAST SOLITONS FOR THE NLS WITH AN EXTERNAL POTENTIAL

We consider the dynamics of a boosted soliton evolving under the cubic NLS with an external potential. We show that for sufficiently large velocities, the soliton is effectively transmitted through the potential. This result extends work of Holmer, Marzuola, and Zworski [11], who considered the case of a delta potential with no bound states, and work of Datchev and Holmer [4], who considered the case of a delta potential with a linear bound state.

Automated summary

We investigate the dynamics of an accelerated soliton in the cubic nonlinear Schrödinger equation with an external potential. We find that for sufficiently large velocities, the soliton can effectively transmit through the potential. This result extends previous studies on delta potentials with or without linear bound states.