Anisotropic subdiffractive solitons

We study solitons in the two-dimensional defocusing nonlinear Schrödinger 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 Schrödinger model and in its averaged amplitude equation.

► 2D nonlinear Schrödinger equation with spatio-temporal potential modulation. ► Microscopic and macroscopic models. ► Stable anisotropic solitons with the lowest lattice symmetry (square). ► Semi-infinite and multibranched stationary solution without detected bistabilities. ► From isotropic to checkered solitons with abrupt unstabilization at low energies.