Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas

By symbolic computation we study a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation describing nonlinear Alfvén waves in inhomogeneous plasmas. Based on the Lax pair of the vc-DNLS equation, the N-fold Darboux transformation is constructed via a gauge transformation and the reduction technique. Multi-solitonic solutions in terms of the double Wronskian for the vc-DNLS equation are obtained. Two- and three-solitonic interactions are analyzed graphically, i.e., overtaking, head-on and parallel interactions. Plasma streaming and inhomogeneous magnetic field control the amplitudes and velocities of the solitonic waves, respectively. The nonuniform density affects the amplitudes of the solitonic waves. The effects of the spectral parameters on the dynamics of the two-solitonic waves are discussed. Our results might facilitate the analytic investigation on certain inhomogeneous systems in the Earth's magnetosphere, solar winds, planetary bow shocks, dusty cometary tails and interplanetary shocks.