Hermite-Gaussian solitons in 1+2 dimensional nonlocal nonlinear systems with Y0-oscillatory response

We investigate the Hermite-Gaussian solitons in 1+2 dimensional nonlocal nonlinear systems with Y0-oscillatory response. The iterative solution of the solitons is numerically found using the accelerated imaginary-time evolution method with amplitude normalization. The existence interval of the solitons is determined based on the boundary conditions, the degree of nonlocality, and the normalized amplitude. The stability of the solitons is demonstrated through a series of numerical simulations. The soliton exhibits breathing behavior during propagation when the incident intensity is increased. The propagation characteristics of higher order Hermite-Gaussian solitons are also investigated.