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| Describing 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. |
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| Keywords:Integrable systems, Solitons, Partial differential equations, Symbolic computation, Nonlinear phenomena |
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