The improved F-expansion method and its application to the MEE circular rod equation and the ZKBBM equation

Md. Shafiqul Islam; M. Ali Akbar; Kamruzzaman Khan

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The improved F-expansion method and its application to the MEE circular rod equation and the ZKBBM equation

機譯：改進的F展開法及其在MEE圓桿方程和ZKBBM方程中的應用

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AbstractIn the present article, we implement the improved F-expansion method combined with Riccati equation to attain traveling wave solutions to nonlinear evolution equations (NLEEs) via the Magneto-electro-elastic circular rod equation and the Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation. We establish three classes of explicit solutions-hyperbolic, trigonometric and rational solutions containing several free parameters. For particular values of the parameters, solitary wave solutions are emanated from the traveling wave solutions. It turns out that, the method is straightforward, concise and it can be applied to many other NLEEs in mathematical physics and engineering.

機譯：摘要在本文中，我們通過磁電彈圓桿方程和Zakharov-Kuznetsov-Benjamin-Bona-Mahony實現了與Riccati方程相結合的改進的F展開方法，以求解非線性演化方程（NLEE）的行波解方程。我們建立了三類顯式解-包含幾個自由參數的雙曲，三角和有理解。對于特定的參數值，行波解產生了孤立波解。事實證明，該方法簡單明了，可應用于數學物理和工程領域的許多其他NLEE。

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《Cogent Mathematics & Statistics》 |2017年第1期|共14頁
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Md. Shafiqul Islam; M. Ali Akbar; Kamruzzaman Khan;
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中圖分類數學;
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1. Applications of extended F-expansion and projective Ricatti equation methods to (2+1)-dimensional soliton equations [J] . Hitender Kumar, Fakir Chand AIP Advances . 2013,第3期

機譯：擴展的F展開和投影Ricatti方程方法在（2 + 1）維孤子方程中的應用
2. An improved generalized F-expansion method and its application to the (2 + 1)-dimensional KdV equations [J] . Sheng Zhang, Tiecheng Xia Communications in Nonlinear Science and Numerical Simulation . 2008,第7期

機譯：改進的廣義F展開方法及其在（2 +1）維KdV方程中的應用
3. A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations [J] . Md. Shafiqul Islam, Kamruzzaman Khan, M. Ali Akbar, Royal Society Open Science . 2014,第2期

機譯：關于改進的 F 展開方法與Riccati方程相結合的說明在非線性發展方程中的應用
4. Improved Generalized F-expansion Method for the time Fractional Modified KdV(fmKdV) Equation [C] . Abdullah Sonmezoglu International Conference of Numerical Analysis and Applied Mathematics . 2016

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5. Discontinuous Galerkin Methods for Convection-Diffusion Equations and Applications in Petroleum Engineering [D] . Chuenjarern, Nattaporn 2019

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6. A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations [O] . Md. Shafiqul Islam, Kamruzzaman Khan, M. Ali Akbar, 2014

機譯：改進的F展開方法與Riccati方程組合用于非線性發展方程的注釋
7. Application of the improved F-expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations [O] . Islam Md. Shafiqul, Khan Kamruzzaman, Akbar M. Ali 2017

機譯：應用改進的F展開方法和Riccati方程找到非線性發展方程的精確解

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The improved F-expansion method and its application to the MEE circular rod equation and the ZKBBM equation

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