TITLE:
Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method
AUTHORS:
Qingmei Zhang, Mei Xiong, Longwei Chen
KEYWORDS:
The First Integral Method, The Partial Differential Equations, The Exact Travelling Wave Solutions
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.1,
January
16,
2020
ABSTRACT: In recent years, many methods have been used to find the exact solutions of nonlinear partial differential equations. One of them is called the first integral method, which is based on the ring theory of commutative algebra. In this paper, exact travelling wave solutions of the Non-Boussinesq wavepacket model and the (2 + 1)-dimensional Zoomeron equation are studied by using the first integral method. From the solving process and results, the first integral method has the characteristics of simplicity, directness and effectiveness about solving the exact travelling wave solutions of nonlinear partial differential equations. In other words, tedious calculations can be avoided by Maple software; the solutions of more accurate and richer travelling wave solutions are obtained. Therefore, this method is an effective method for solving exact solutions of nonlinear partial differential equations.