Integrable properties for a variable-coefficient Boussinesq equation from weakly nonlinear dynamics with symbolic computation
首发时间:2007-11-14
Abstract: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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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
摘要:本文研究一类用于描述在顺流方向上存在可变剪切流动的长波的变系数Boussinesq方程。利用计算机符号计算,在系数函数满足一定的约束条件下,将变系数方程变换到相应的常系数方程。接下来,利用所得变换可得到原变系数方程一系列可积性质,例如自Bäcklund变换、非线性叠加公式、Lax对、Darboux变换等。此外,根据所得的可积性质还可以求得变系数Boussinesq方程的孤子型解。最后,对所得解可能存在的相关物理应用进行了讨论。
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No.1633911149111950****
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