3 papers
math.AP2026
Modeling soliton-potential interactions for the 1-D cubic NLS via an invariant-preserving finite-difference method
Anthony D. Stone, Christopher C. Hogan
We consider the 1-D focusing cubic NLS with a smooth, spatially-dependent potential which decays rapidly as . As is well known, under sufficient regularit…
math.AP2023
Transmission of fast solitons for the NLS with an external potential
Christopher C. Hogan, Jason Murphy
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 tr…
math.AP2022
Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation
Christopher C. Hogan, Jason Murphy, David Grow
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 gi…