Accessible soliton solutions with initial phase-front curvature in strongly nonlocal nonlinear media

Based on the extended fractional dimensional nonlinear Schrödinger equation and the variable separation method, a fractional accessible soliton solution with initial phase curvature is proposed for the first time. The soliton solution of the model is composed of hypergeometric functions and generalized Laguerre polynomials in fractional dimensional space, namely, Hypergeometric-Laguerre-Gaussian soliton. The theoretical results indicate that a series of different types of solitons are generated with the change of the beam parameters, forming a fractious family of solitons. At the same time, solitons produce a splitting phenomenon similar to that of the Hermitian beams. Additionally, the initial phase curvature also affects the stability of beam propagation, suppressing the formation of soliton.