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

Abstract EN

The relations between Dp-operators andmultidimensional binary Bell polynomials are explored and appliedto construct the bilinear forms with Dp-operators of nonlinear equationsdirectly and quickly.

Exact periodic wave solution of a(3+1)-dimensional generalized shallow water equation is obtainedwith the help of the Dp-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.