An perturbation-iteration method for multi-peak solitons in nonlocal nonlinear media

TL;DR

This paper introduces a perturbation-iteration method for efficiently computing multi-peak Hermite-Gaussian-like solitons in nonlocal nonlinear media, with potential applications to Schrödinger equations in various potentials.

Contribution

A novel perturbation-iteration approach for calculating multi-peak solitons in nonlocal media, improving accuracy and efficiency over existing methods.

Findings

Requires only a few tens of iterations for high accuracy

Uses Hermite-Gaussian functions as initial conditions

Potential extension to Schrödinger equations in different potentials

Abstract

An perturbation-iteration method is developed for the computation of the Hermite-Gaussian-like solitons with arbitrary peak numbers in nonlocal nonlinear media. This method is based on the perturbed model of the Schr\"{o}dinger equation for the harmonic oscillator, in which the minimum perturbation is obtained by the iteration. This method takes a few tens of iteration loops to achieve enough high accuracy, and the initial condition is fixed to the Hermite-Gaussian function. The method we developed might also be extended to the numerical integration of the Schr\"{o}dinger equations in any type of potentials.