Solitonic interaction and Pfaffianization for a (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid

Under investigation in this paper is a (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation, which is used for the interfacial waves in a two-layer liquid. Based on the bilinear forms, we obtain the bilinear Bäcklund transformation which differs from those previous reported for such an equation. We obtain the N-kink soliton solutions in the Gramian. Two elastic and inelastic oblique kink solitons are shown. Two elastic parallel kink solitons are also presented. Furthermore, based on the Pfaffianization, Wronski- and Gram-type Pfaffian solutions for a Pfaffianized coupled (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama system are derived.