Z. Naturforsch. 68a, 235 – 244
Solitons for a Forced Extended Korteweg–de Vries Equation with Variable Coefficients in Atmospheric Dynamics
State Key Laboratory of Information Photonics and Optical Communications and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Received March 30, 2012 / revised August 23, 2012 / published online March 11, 2013
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. One- and 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.
Key words: Forced Extended Korteweg–de Vries Equation in Atmospheric Dynamics; Integrability; Soliton Solutions; Symbolic Computation; Binary Bell Polynomial.
PACS numbers: 05.45.Yv; 42.65.Tg; 42.81.Dp; 02.30.Ik