Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation

摘要

The relations betweenDp-operators andmultidimensional binary Bell polynomials are explored and appliedto construct the bilinear forms withDp-operators of nonlinear equationsdirectly and quickly. Exact periodic wave solution of a(3+1)-dimensional generalized shallow water equation is obtainedwith the help of theDp-operators and a general Riemann thetafunction in terms of the Hirota method, which illustrate that bilinearDp-operators can provide a method for seeking exact periodic solutionsof nonlinear integrable equations. Furthermore, the asymptoticproperties of the periodic wave solutions indicate that the solitonsolutions can be derived from the periodic wave solutions.