Solitons for a Forced Extended Korteweg–de Vries Equation with Variable Coefficients in Atmospheric Dynamics

Under investigation is a forced extended Korteweg–de Vries equation with variable coefficients, which can describe the atmospheric blocking phenomenon. The nonisospectral Lax pair for this equation is constructed via symbolic computation, and new integrable conditions are given. Oneand two-soliton solutions are derived explicitly through the binary-Bell-polynomial method under the integrable conditions. Based on the solutions, kink-type and bell-profile-like (BPL) solitons are obtained under certain conditions. The analysis shows that the variable coefficients not only influence the amplitudes and velocities of the kink-type and BPL solitons, but also affect the background and the type of interaction.