Anisotropic Subdiffractive Solitons

TL;DR

This paper investigates anisotropic solitons in a 2D defocusing nonlinear Schrödinger equation with a square lattice potential, revealing their formation in both the original and averaged models, and highlighting the effects of anisotropic diffraction.

Contribution

It introduces the concept of anisotropic solitons in a 2D nonlinear Schrödinger equation with a square lattice potential, demonstrating their existence in both original and averaged models.

Findings

Anisotropic solitons exist in the 2D defocusing nonlinear Schrödinger equation.

Solitons with square (x,y)-geometry are obtained.

Anisotropic diffraction effects are characterized in the models.

Abstract

We study solitons in the two-dimensional defocusing nonlinear Schroedinger equation with the spatio-temporal modulation of the external potential. The spatial modulation is due to a square lattice; the resulting macroscopic diffraction is rotationally symmetric in the long-wavelength limit but becomes anisotropic for shorter wavelengths. Anisotropic solitons -- solitons with the square (x,y)-geometry -- are obtained both in the original nonlinear Schroedinger model and in its averaged amplitude equation.