Bright soliton solutions to a nonlocal nonlinear Schrodinger equation of reverse-time type

Two types of multiple bright soliton solutions for a focusing nonlocal reverse-time nonlinear Schrodinger equation are derived by using the Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction. Compared with the case of the local Manakov system, both types of soliton solutions are restricted to ones with even numbers. For the first type of solution, the fundamental paired soliton exhibits two paralleled line solitons along with the time axis and the special breathing soliton. For the second type of solution, the fundamental paired soliton only allows head-on collisions with the same velocity, in which the collision with spatial interferences and the degenerate soliton with position shifts can be realized with certain parameters. General higher-order soliton solutions of two types describe the superposition of the fundamental paired soliton, which show a few interesting dynamical behaviors such as the superposed breathing solitons, the interaction of two paired soliton bound states, the interaction of two degenerate solitons with position shifts and the breathing soliton with position shifts.