Solitons, Backlund transformation and Lax pair for a generalized variable-coefficient Boussinesq system in the two-layered fluid flow

摘要

Under investigation in this paper is a generalized variable-coefficient Boussinesq system, which describes the propagation of the shallow water waves in the two-layered fluid flow. Bilinear forms, Backlund transformation and Lax pair are derived by virtue of the Bell polynomials. Hirota method is applied to construct the one-and two-soliton solutions. Propagation and interaction of the solitons are illustrated graphically: kink-and bell-shape solitons are obtained; shapes of the solitons are affected by the variable coefficients alpha(1), alpha(3) and alpha(4) during the propagation, kink-and anti-bell-shape solitons are obtained when alpha(3) > 0, anti-kink-and bell-shape solitons are obtained when alpha(3) < 0; Headon interaction between the two bidirectional solitons, overtaking interaction between the two unidirectional solitons are presented; interactions between the two solitons are elastic.