Solitons and bilinear Bäcklund transformations for a (3+1)(3+1)-dimensional Yu–Toda–Sasa–Fukuyama equation in a liquid or lattice

In this paper, we investigate a (3+1)(3+1)-dimensional Yu–Toda–Sasa–Fukuyama equation for the interfacial wave in a two-layer liquid or elastic quasiplane wave in a lattice. Through the Bell polynomials, symbolic computation and Hirota method, the one and two bell-soliton solutions are derived. Bäcklund transformation is presented. Parallel collision between the two solitons exists when the soliton directions are the same. Oblique collision appears between the two solitons with different soliton directions.