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.