Analyzing the combined multi-waves polynomial solutions in a two-layer-liquid medium

In this work, we investigate the behavior of mixed wave solutions in two-layer-liquid with dispersive waveguide. These combined multi-wave solutions were obtained in polynomial types for the (3 + 1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation with variable coefficients. By virtue of the generalized unified method and symbolic computations, we formally derive polynomial solutions for this equation. The obtained solutions include multi-soliton solutions, multi-periodic solutions, and multi-elliptic solutions. Furthermore, the physical insight and the movement role of the waves in the two-layers are discussed and analyzed graphically for different selections of the arbitrary functions of the obtained solutions.