Homogenization for the nonlinear Schr\"odinger equation with sprinkled nonlinearity
Benjamin Harrop-Griffiths, Maria Ntekoume
TL;DR
This paper proves homogenization for a nonlinear Schr"odinger equation with sprinkled nonlinearity and studies the fluctuations of solutions around the homogenized solution.
Contribution
It introduces a homogenization result for the nonlinear Schr"odinger equation with sprinkled nonlinearity and analyzes solution fluctuations.
Findings
Homogenization established for the nonlinear Schr"odinger equation with sprinkled nonlinearity.
Analysis of fluctuations around the homogenized solution.
Provides foundational results for equations with sprinkled nonlinearities.
Abstract
We first prove homogenization for the nonlinear Schr\"odinger equation with sprinkled nonlinearity introduced in [19]. We then investigate how solutions fluctuate about the homogenized solution.
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