Integrability aspects and soliton solutions for an inhomogeneous nonlinear system with symbolic computation

Under investigation in this paper is an inhomogeneous nonlinear system, which describes the marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics under inhomogeneous media. Through symbolic computation, the Painleve integrable condition, Lax pair and conservation laws are derived for this system. Furthermore, by virtue of the Darboux transformation, the explicit multi-soliton solutions are generated. Figures are plotted to reveal the following dynamic features of the solitons: (1) Parallel propagation of solitons: separation distance of the two parallel solitons depends on the value of vertical bar Im(lambda(1))vertical bar - vertical bar Im(lambda(2))vertical bar (where lambda(1) and lambda(2) are the spectrum parameters); (2) Periodic propagation of bound solitons: periodic bound solitons taking on contrary trends, and mutual attractions and repulsions of two bright bound solitons; (3) Elastic interactions of two one-peak bright solitons and of two one-peak dark solitons. (C) 2011 Elsevier B.V. All rights reserved.