Sudao Bilige, Wang Xiaomin
College of Sciences, Inner Mongolia University of Technology, Hohhot, Inner Mongolia, PR China.
PLoS One. 2015 May 14;10(5):e0126635. doi: 10.1371/journal.pone.0126635. eCollection 2015.
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
本文提出了一种广义最简方程法来求解非线性演化方程（NLEEs）的精确解。在该方法中，我们选择了一个具有变系数的解表达式和一个变系数常微分辅助方程。此方法能够在非线性演化方程与一个相关约束方程之间产生一个贝克隆变换。通过处理该约束方程，我们可以为非线性演化方程导出无穷多个精确解。这些解包括行波解、非行波解、多孤子解、有理解以及其他类型的解。作为应用，我们运用广义最简方程法得到了Boussinesq - Burgers方程的大量精确解。
