Bright and dark wirelike spatiotemporal solitons of a partially nonlocal nonlinear Schrödinger equation

A (3+1)-dimensional nonautonomous partially nonlocal nonlinear Schrödinger equation with different diffractions is reduced to an autonomous nonlinear Schrödinger equation. Based on solutions of the autonomous nonlinear Schrödinger equation, and using the Darboux transformation method, spatiotemporal bright and dark soliton solutions are obtained. Dynamical evolution of wirelike spatiotemporal bright and dark single soliton, separated and interactive wirelike wave bright and dark double soliton structures are discussed in the sinusoidal diffraction system. For specified value of the parameter n in the Hermite polynomial, bright and dark single soliton, parallel separated bright and dark double soliton and interactive bright and dark double soliton structures all exist n+1 columns in z-direction.