Analytic study on the Sawada–Kotera equation with a nonvanishing boundary condition in fluids

Under investigation in this paper is the Sawada–Kotera equation with a nonvanishing boundary condition, which describes the evolution of steeper waves of shorter wavelength than those described by the Korteweg–de Vries equation does. With the binary-Bell-polynomial, Hirota method and symbolic computation, the bilinear form and N-soliton solutions for this model are derived. Meanwhile, propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis. Via Bell-polynomial approach, the Bäcklund transformation is constructed in both the binary-Bell-polynomial and bilinear forms. Based on the binary-Bell-polynomial-type Bäcklund transformation, we obtain the Lax pair and conservation laws associated.

► We derive the Bell-polynomial forms and N-soliton solutions for SK–NB equation .
► Graphical illustrations on the soliton solutions for SK–NB equation are presented.
► Based on the BT, we obtain the Lax pair for SK–NB equation.
► We derive conservation laws for SK–NB equation based on Bell-polynomial-type BT.