Solitary Wave and Doubly Periodic Wave Solutions to Three-Dimensional Nizhnik-Novikov-Veselov Equation

The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutionsexactly degenerate to the soliton solutions at a certain limit condition.Compared with the existing tanh methods and Jacobi function method, themethod we used here gives more general exact solutions without much extraeffort.