Multi-breather wave solutions for a generalized (3＋1)-dimensional Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid

Two-layer fluid models are proposed to describe certain nonlinear phenomena in fluid mechanics, thermodynamics and medical sciences. For a generalized(3＋1)-dimensional Yu–Toda–Sasa–Fukuyama equation for the interfacial waves in a two-layer liquid, in which h₀ is the constant coefficient of the development term, h₁ is the constant coefficient of the dispersion term, h₂ and h₃ are the constant coefficients of the nonlinear terms, and h₄ is the constant coefficient of the linear term. Based on the Pfaffian technique and certain constraint on h₃, we obtain the multi-breather solutions in terms of the Gramian. For the one-breather waves, amplitudes are proportional to [Formula presented], velocity components along the x and z directions for the characteristic lines are proportional to [Formula presented], and velocity component along the y direction for the characteristic line is proportional to [Formula presented], where x, y and z are the spatial coordinates and t is the temporal coordinate. Interaction between the two-breather waves implies that the two-breather waves can evolve periodically along two straight lines on the x-y and y-z planes, period for the two-breather waves with t is proportional to [Formula presented], period for the two-breather waves along the y direction is proportional to [Formula presented], while the two-breather waves are not periodic along the x and z directions. Amplitudes, velocities and widths of the two-breather waves keep unchanged after the interaction between the two-breather waves on the x-y and y-z planes, which means that the interaction is elastic. On the x-z plane, the two-breather waves appear as two parallel solitons at certain angles with the x and z axes.