Periodic-wave and semi-rational solutions for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

This paper investigates the periodic-wave and semi-rational solutions in determinant form for the (3 + 1)-dimensional Yu-Toda-Sasa-Fukuyama equation via the Kadomtsev-Petviashvili hierarchy reduction. By analyzing the periodic-wave solutions' properties, we obtain a breather on the x-y plane (or y - z plane) and two kinds of periodic waves on the x - z plane. One of the periodic waves is of growing-decaying amplitude, and the other one is of invariant amplitude. The breather always parallels with the x-direction, and its characteristic lines decide the evolution of the breather. By taking the long-wave limit on the periodic-wave solutions, we derive semi-rational solutions, which generate a lump on the x-y plane and a line rogue wave or moving soliton the x - z plane. Based on the relationship between these two solutions, we conclude that (1) the lump is the limit on the breather; (2) the soliton is the limit of the amplitude-invariant periodic wave; (3) the rogue wave is the limit of the growing-decaying periodic wave. (C) 2021 Elsevier Ltd. All rights reserved.