Author(s)

Minghuan Liu, Yuanguang Zheng

College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China.

In this paper, we study an elliptic equation with four distinct real roots and obtain five new solutions to this type of elliptic equation. Using these obtained new elliptic function solutions we can construct a series of explicit exact solutions for many nonlinear evolution equations. As examples, we choose combined KdV-MKdV equation, a fourth-order integrable nonlinear Schrödinger equation and generalized Dullin-Gottwald-Holm equation to demonstrate the effectiveness of these new elliptic function solutions. These new elliptic function solutions can be applied to many other nonlinear evolution equations.

Elliptic Equation, Periodic Wave Solution, Singular Wave Solution, Combined KdV-MKdV Equation, Generalized Dullin-Gottwald-Holm Equation

Liu, M. and Zheng, Y. (2022) New Solutions for an Elliptic Equation Method and Its Applications in Nonlinear Evolution Equations. Journal of Applied Mathematics and Physics, 10, 2415-2431. doi: 10.4236/jamp.2022.108164.