Rational solutions of the classical Boussinesq–Burgers system
Rational solutions of the classical Boussinesq–Burgers system
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DOI：
10.1007/s11071-018-4424-6
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发表时间：
2018-06
影响因子：
5.6
通讯作者：
Ming Li;Wenkai Hu;Chengfa Wu
中科院分区：
文献类型：
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作者：
Ming Li;Wenkai Hu;Chengfa Wu
研究了描述浅水波传播的经典Boussinesq-Burgers（CBB）方程组的有理解。在这项工作中应用的主要工具，以获得这些解决方案是双线性方法和Kadomtsev Petviashvili层次结构减少技术。其解用行列式形式给出，行列式的矩阵元素与舒尔多项式有关，并具有简单的代数表达式。此外，这些合理的解决方案的动力学研究分析和图形。对于不同的CBB系统参数值，解可以描述双峰（M形）波或单峰波的相互作用。结果还表明，根据解中自由参数的选择，相互作用波的最大振幅可能高于或低于碰撞前的振幅。此外，某些有理解在特殊的参数选择下可能在有限时刻爆破到无穷大。
We study rational solutions of the classical Boussinesq–Burgers (CBB) system which describes the propagation of shallow water waves. The main tools applied in this work to derive these solutions are the bilinear method and the Kadomtsev–Petviashvili hierarchy reduction technique. The solutions are given in terms of determinants whose matrix elements are related to Schur polynomials and have simple algebraic expressions. Moreover, the dynamics of these rational solutions are investigated analytically and graphically. For different values of the parameter coming from the CBB system, the solutions may describe the interaction of double-peak (M-shape) waves or single-peak waves. It is also shown that, depending on the choices of free parameters in the solutions, the maximum amplitude of the interaction wave could be higher or lower than the amplitudes before collision. In addition, some of the rational solutions may blow up to infinity at finite time under special choices of parameters.