arXiv subjects

Christopher C. Hogan

Publications and source records attributed to Christopher C. Hogan.

2 recordsLinked to original sources

arXiv2023

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, who considered the case of a delta potential with no bound states, and work of Datchev and Holmer, who considered the case of a delta potential with a linear bound state.

math.AP↗

arXiv2022

Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation

We consider the problem of recovering a spatially-localized cubic nonlinearity in a nonlinear Schrödinger equation in dimensions two and three. We prove that solutions with data given by small-amplitude wave packets accrue a nonlinear phase that determines the X-ray transform of the nonlinear coefficient.

math.AP↗