Soliton solutions to the reverse-time nonlocal Davey–Stewartson III equation

This study derives solitons solutions of the reverse-time nonlocal Davey–Stewartson III equation by the Kadomtsev–Petviashvili hierarchy reduction method and Hirota’s bilinear method. The solutions are expressed as N×N Gram-type determinants with different parametric reduction conditions. N-soliton and line breather solutions on both constant and periodic backgrounds are derived. The dynamics of these solutions are discussed. All possible configurations of these solutions are illustrated for 1≤N≤4. Both intersecting and parallel solitons are presented. In particular, the elastic and inelastic collisions of the two parallel-soliton solutions are determined. In the inelastic case, the amplitudes of the solitons change after collision. Moreover, the parametric conditions for determining the inelastic collisions are derived, and all possible types of inelastic behaviors are obtained and displayed. •N-soliton solutions on constant and periodic backgrounds are obtained.•Interesting inelastic collisions between solitons are discussed in detail.•Breather solutions on constant and periodic backgrounds are obtained.