时空分数阶双Sine-Gordon方程的显式精确解
Explicit Exact Solutions of Space-Time Fractional Double Sine-Gordon Equation
摘要: 本文结合变量分离的ODE方法和一个复变换，通过找到一个合适且易于求解的辅助方程，构造出带有conformable分数阶导数的双Sine-Gordon方程一些新的精确解，丰富了其精确解解系。同时表明该方法高效简洁，可应用于求解其他同类型分数阶偏微分方程。
Abstract: In this paper, combing the variable separated ODE method and a complex transformation, we constructed some new exact solutions of the double Sine-Gordon equation with conformable fractional derivative. Especially, we found a suitable auxiliary equation which can be solved easily and powerful for enriching its exact solution system. It is shown that this method is efficient and simple. Thus, the used method is highly recommended to solve other fractional partial differential equations of the same type.
文章引用：林鸿夸. 时空分数阶双Sine-Gordon方程的显式精确解[J]. 应用数学进展, 2021, 10(3): 689-693. https://doi.org/10.12677/AAM.2021.103075

参考文献

[1] Beal, R., Rabelo, M. and Tenenblat, K. (1988) Bäcklund Transformations and Inverse Scattering and for Some Pseudo-Spherical Surface Equations. Studies in Applied Mathematics, 81, 125-151. [Google Scholar] [CrossRef] 
[2] Shang, Y.D., Huang, Y. and Yuan, W.J. (2011) Bäcklund Transformations and Abundant Exact Explicit Solutions of the Sharma-Tasso-Olver Equation. Applied Mathematics and Computation, 217, 7172-7183. [Google Scholar] [CrossRef] 
[3] Bayrak, M.A. (2018) Anosov Application of the G’/G-Expansion Method for Some Space-Time Fractional Partial Differential Equations. Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 67, 60-67. [Google Scholar] [CrossRef] 
[4] Zhu, S.D. (2010) The Extended G’/G-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations. Mathematical and Computational Applications, 15, 924-929. [Google Scholar] [CrossRef] 
[5] Lu, D.C. and Zhang, Z.H. (2017) Exact Solutions for Fractional Nonlinear Evolution Equations by the F-Expansion Method. International Journal of Nonlinear Science, 24, 180-187.
[6] Shang, Y.D. (2008) The Extended Hyperbolic Function Method and Exact Solutions of the Long-Short Waveresonance Equations. Chaos, Solitons & Fractals, 36, 762-771. [Google Scholar] [CrossRef] 
[7] Wazwaz, A.M. (2004) A Sine-Cosine Method for Handling Nonlinear Wave Equation. Mathematical and Computer Modelling, 40, 499-508. [Google Scholar] [CrossRef] 
[8] Wang, M.L. and Li, X.Z. (2006) Exact Solutions to the Double Sine-Gordon Equation. Chaos, Solitons & Fractals, 27, 477-486. [Google Scholar] [CrossRef] 
[9] Zhang, S. and Zhang, H.Q. (2011) Fractional Sub-Equation Method and Its Applications to Nonlinear fractional PDEs. Physics Letters A, 375, 1069-1073. [Google Scholar] [CrossRef] 
[10] Wazwaz, A.M. (2005) Exact Solutions to the Double Sinh-Gordon Equation by the Tanh Method and a Variable Separated ODE Method. Computers & Mathematics with Applications, 50, 499-508. [Google Scholar] [CrossRef] 
[11] Sun, Y.C. (2015) New Exact Traveling Wave Solutions for Double Sine-Gordon Equation. Applied Mathematics and Computation, 258, 100-104. [Google Scholar] [CrossRef] 
[12] Dai, C.Q., Cen, X. and Wu, S.S. (2009) Exact Travelling Wave Solutions of the Discrete Sine-Gordon Equation Obtained via the Exp-Function Method. Nonlinear Analysis, 70, 58-63. [Google Scholar] [CrossRef] 
[13] Hosseini, K., Mayeli, P. and Kumar, D. (2018) New Exact Solutions of the Coupled Sine-Gordon Equations in Nonlinear Optics Using the Modified Kudryashov Method. Journal of Modern Optics, 65, 361-364. [Google Scholar] [CrossRef] 
[14] Khalil, R., Al Horani, M., Yousef, A., et al. (2014) A New Definition of Fractional Derivative. Journal of Computational and Applied Mathematics, 264, 65-70. [Google Scholar] [CrossRef] 

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