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-Backlund 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. (c) 2021 Published by Elsevier Ltd.

Automated summary

This study examines a (2+1)-dimensional generalized variable coefficient Boiti-Leon-Pempinelli system for water waves, and constructs a set of hetero-Backlund transformations and similarity reductions through scaling transformations and symbolic computation. These link the original system to a known generalized variable-coefficient Burgers equation and an ordinary differential equation, respectively, depending on the variable coefficients in the original system.