Perturbation-iteration method for multi-peak solitons in nonlocal nonlinear media

A 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 Schrodinger 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 Schrodinger equations in any type of potentials.