Variable separation solutions to the integrable higher order Broer–Kaup (HBK) system in (2+1)-dimensional spaces

Starting from the Bäcklund transformation and using Cole–Hopf transformation, we reduce the integrable higher order Broer–Kaup (HBK) system in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t}. Then we obtain some new solutions of the original equations by investigating the simple linear evolution equation which include the solutions obtained by the variable separation approach.