Rational solutions of the classical Boussinesq-Burgers system

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.