Computation of minimum action paths of the stochastic nonlinear Schroedinger equation with dissipation

TL;DR

This paper applies the geometric minimum action method to compute transition paths in the dissipative nonlinear Schrödinger equation, linking PDE minimizers to finite-dimensional reductions for solitary wave transitions.

Contribution

It introduces a novel application of the geometric minimum action method to dissipative nonlinear Schrödinger equations and explores the connection between PDE and finite-dimensional minimizers.

Findings

Successfully computed minimizers for dissipative Schrödinger equations.

Established relationship between PDE minimizers and finite-dimensional reductions.

Provided insights into solitary wave transition pathways.

Abstract

Using the geometric minimum action method, we compute minimizers of the Freidlin-Wentzell functional for the dissipative linear and nonlinear Schroedinger equation. For the particular case of transitions between solitary waves of different amplitudes, we discuss the relationship of the minimizer of the PDE model to the minimizer of a finite-dimensional reduction.