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A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

机译：广义最简单方程法及其在Boussinesq-Burgers方程中的应用

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摘要

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.

机译：本文提出了一种广义最简单方程方法，以寻求非线性演化方程（NLEE）的精确解。在该方法中，我们选择了具有可变系数和可变系数常微分辅助方程的解表达式。该方法可以在NLEE和相关的约束方程之间产生Bäcklund变换。通过处理约束方程，我们可以得出无限数量的NLEE精确解。这些解决方案包括行波解决方案，非行波解决方案，多孤子解决方案，有理解决方案以及其他类型的解决方案。作为应用，我们通过使用广义最简单方程方法获得了Boussinesq-Burgers方程的大量精确解。

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期刊名称 other
作者
Bilige Sudao; Xiaomin Wang;
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年(卷),期 -1(10),5
年度 -1
页码 e0126635
总页数 12
原文格式 PDF
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1. A generalization of the simplest equation method and its application to (3t1)- dimensional KP equation and generalized Fisher equation [J] . Zhonglong Zhao, Yufeng Zhang, Zhong Han, Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2014,第7期

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2. On the class of nonlinear PDEs that can be treated by the modified method of simplest equation. Application to generalized Degasperis-Processi equation and b-equation [J] . Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov Communications in Nonlinear Science and Numerical Simulation . 2011,第8期

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3. Application of the Generalized Simplest Equation Method to the Burgers Equation [J] . Yuexing Bai, Sudao Bilige, Xiaoqing Gao, Journal of Applied Mathematics and Physics . 2017,第1期

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4. Solutions of a Generalized Complexly Coupled Korteweg-de Vries System Using Simplest Equation Method [C] . Khalique Chaudry Masood International Conference on Computational Science and Computational Intelligence . 2014

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5. Generalized profiling method and the applications to adaptive penalized smoothing, generalized semiparametric additive models and estimating differential equations. [D] . Cao, Jiguo. 2006

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6. General Approach to Coupled Reactive Smoluchowski Equations: Integration and Application of DVR and Generalized Coordinate Methods to Diffusive Problems [O] . Andrea Piserchia, Shiladitya Banerjee, Vincenzo Barone -1

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7. A generalized simplest equation method and its application to the Boussinesq-Burgers equation. [O] . Bilige Sudao, Xiaomin Wang 2015

机译：广义最简单方程方法及其在Boussinesq-Burgers方程中的应用。

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

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