Mixed-type soliton propagations in two-layer-liquid (or in an elastic) medium with dispersive waveguides

Abstract

In this paper the behavior of mixed two-soliton solutions of the (3+1)-dimensional Yu–Toda–Sasa–Fukuyama (YTSF) equation with variable coefficients in two-layer liquid (or in an elastic) medium are shown. Indeed, this equation shows two types of dispersive, namely longitudinal and lateral dispersion. Also, it shows flux transport in x and z-directions that arises from the nonlinear term. The geometric structure of solutions for the behavior of the propagation of the mixed-soliton waves may be characterized as in what it follows. (i) In Case when the longitudinal-dispersion coefficient is periodic. It is found that in the upper layer two-soliton waves mixed with a shock wave are propagating in the x-direction. While in the lower layer two-antisoliton waves mixed with a shock wave are propagating. In the both two layers the waves are periodic in time. This may be argued to the strong-coupling that arises from the dominance of the longitudinal dispersive. While in the y-direction two-soliton and two-antisoliton waves are propagating in the upper and lower layers respectively. The flux transport in z-direction results to propagate train of two-soliton and two-antisoliton waves in the upper and lower layers respectively. (ii) When the coefficients of the coupling of the flux transport and dispersions are taken to increase of propagation for solitons occurs but with gaps. (iii) When the dispersion coefficient is a solitary wave, it is found that propagation of two-soliton waves incoming in the upper layer while two-antisoliton waves outgoing in the lower layer.