The nonlinear Schr\"odinger equation with sprinkled nonlinearity
Benjamin Harrop-Griffiths, Rowan Killip, Monica Visan
TL;DR
This paper proves the global well-posedness of a nonlinear Schrödinger equation where the nonlinearity is randomly distributed according to a Poisson process, advancing understanding of stochastic effects in nonlinear PDEs.
Contribution
It introduces a novel analysis of the nonlinear Schrödinger equation with nonlinearity concentrated on a Poisson process, establishing global well-posedness in this stochastic setting.
Findings
Proved global well-posedness for the stochastic NLS with sprinkled nonlinearity.
Extended deterministic NLS theory to a stochastic, Poisson-driven context.
Demonstrated stability of solutions under random nonlinearity distribution.
Abstract
We prove global well-posedness for the cubic nonlinear Schr\"odinger equation with nonlinearity concentrated on a homogeneous Poisson process.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Quantum Mechanics and Non-Hermitian Physics