基于符号计算的弱非线性动力学中变系数Boussinesq方程的可积性质研究

escribing the weakly nonlinear dynamics of long waves embedded in marginally stable shear flows that vary in the streamwise direction, a variable-coefficient Boussinesq equation is investigated in this paper. With symbolic computation, such a model is transformed into its constant-coefficient counterpart under certain constraints on the coefficient functions. By virtue of the obtained transformation, some integrable properties for this equation are derived, such as the auto-Bäcklund transformation, nonlinear superposition formula, Lax pair and Darboux transformation. In addition, some soliton-like solutions are obtained from the integrable properties and the relevant physical applications are also pointed out.