Sparsifying preconditioner for soliton calculations

TL;DR

This paper introduces a new computational method combining a sparsifying preconditioner with Newton's method to efficiently compute solitons in nonlinear Schrödinger equations, demonstrated through optical gap soliton examples.

Contribution

The paper presents a novel, robust computational approach that enhances soliton calculation efficiency using a sparsifying preconditioner with Newton's method.

Findings

Efficient computation of gap solitons demonstrated

Method outperforms traditional approaches in robustness and speed

Applicable to nonlinear optics problems

Abstract

We develop a robust and efficient method for soliton calculations for nonlinear Schr\"odinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of the method is demonstrated by numerical examples of gap solitons in the context of nonlinear optics.