Symbolic computation on a ( 2 + 1 )-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system for the water waves

Water waves attract people's attention. For the water waves, a ($2+1$)-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system is hereby studied. As for the horizontal velocity and elevation of the water wave, on the one hand, with the scaling transformations and symbolic computation, a set of the hetero-Bäcklund transformations is constructed, linking the original system with a known generalized variable-coefficient Burgers equation. As for the horizontal velocity and elevation of the water wave, on the other hand, with symbolic computation, a set of the similarity reductions is constructed, from the original system to a known ordinary differential equation. All our results depend on the variable coefficients in the original system.