Variational approach to multidimensional solitons in highly nonlocal nonlinear media

TL;DR

This paper compares variational and accessible soliton approximations for multidimensional solitons in highly nonlocal nonlinear media, demonstrating that the variational approach yields more accurate results across 1D, 2D, and 3D cases.

Contribution

The study introduces a variational method for analyzing multidimensional solitons in highly nonlocal media and shows its superior accuracy over the accessible soliton approximation.

Findings

Variational approach outperforms accessible soliton approximation in accuracy.

The variational method is effective in 1D, 2D, and 3D systems.

Numerical solutions confirm the improved precision of the variational method.

Abstract

We apply the variational approach to solitons in highly nonlocal nonlinear media in $D=1,2,3$ dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the variational highly nonlocal approximation provides more accurate results and as such is more appropriate solution than the accessible soliton approximation.