On a generalized Broer-Kaup-Kupershmidt system for the long waves in shallow water

Describing the long waves in shallow water, a generalized Broer-Kaup-Kupershmidt system is investigated in this paper. With respect to the horizontal velocity of the water wave and the height of the water surface, we use symbolic computation to build up (A) a scaling transformation, (B) a set of the hetero-Backlund transformations, from that generalized system to a known linear partial differential equation, as well as (C) two sets of the similarity reductions, each of which from that generalized system to a known ordinary differential equation. Our results depend on all the shallow-water coefficients for that generalized system.

Automated summary

This paper investigates a generalized Broer-Kaup-Kupershmidt system describing long waves in shallow water. By using symbolic computation, the authors establish a scaling transformation, a set of hetero-Backlund transformations, and two sets of similarity reductions from the generalized system to known linear and ordinary differential equations. The results depend on all the shallow-water coefficients.