Integrability and Solutions of the (2+1)-Dimensional Broer—Kaup Equation with Variable Coefficients

The integrability of the (2+1)-dimensional Broer—Kaup equation with variable coefficients (VCBK) is verified by finding a transformation mapping it to the usual (2+1)-dimensional Broer—Kaup equation (BK). Thus the solutions of the (2+1)-dimensional VCBK are obtained by making full use of the known solutions of the usual (2+1)-dimensional BK. Two new integrable models are given by this transformation, their dromion-like solutions and rogue wave solutions are also obtained. Further, the velocity of the dromion-like solutions can be designed and the center of the rogue wave solutions can be controlled artificially because of the appearance of the four arbitrary functions in the transformation.