Rogue-wave, rational and semi-rational solutions for a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation in a two-layer fluid

Two-layer-fluid models are used to describe certain nonlinear phenomena in medical science and fluid mechanics. Under investigation in this paper is a generalized (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation for the interfacial waves in a two-layer fluid. Rogue-wave, rational and semi-rational solutions are given via the Kadomtsev-Petviashvili hierarchy reduction. We discuss the influence of the coefficients in that equation on the semi-rational solutions. For the first-order semi-rational solutions, we derive that: (1) when h> 0 , the lump catches up with the soliton, and then the lump merges into the soliton; when h< 0 , the lump appears from the soliton and then separates from the soliton; (2) the amplitudes of the soliton and lump decrease with h₁ decreasing; (3) the amplitudes of the soliton and lump decrease with h₂ increasing; (4) the lump becomes narrower with h₄ decreasing, where h0,h1,h2 and h₄ are the constant coefficients in that equation.