title: The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.
abstract: In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.
authors.affiliation: College of Sciences, Inner Mongolia University of Technology, Hohhot, 010051 China.
authors.forename: Litao
authors.initials: L
authors.lastname: Gai
authors.affiliation: College of Sciences, Inner Mongolia University of Technology, Hohhot, 010051 China.
authors.forename: Sudao
authors.initials: S
authors.lastname: Bilige
authors.affiliation: College of Sciences, Dalian University of Technology, Dalian, 116024 China.
authors.forename: Yingmo
authors.initials: Y
authors.lastname: Jie
keywords: Symmetry; The extended tanh method; The homotopy perturbation method; Wu-differential characteristic set algorithm