Hyperbolic and exponential solutions to the coupled Sine-Gordon system

References

• K.B. Oldham, J. Spanier, The Fractional Calculus, Academic press, New York (1974).
   Google Scholar
• K.S. Miller, B. Ross, An Introduction to the Fractional and Fractional Differential Equations, John Wiley and Sons, New York (1993).
   Google Scholar
• Y. Luchko, R. Gorenflo, The initial-value problem for some fractional differential equations with Caputo derivative, Preprint Series A08-98, Fachbereich Mathematik and Informatic, Freie Universitat, Berlin (1998).
   Google Scholar
• I. Podlubny, Fractional Differential Equations, Academic press, New York (1999).
   Google Scholar
• EL-Wakil, S.A., Madkour, M.A., Abdou, M.A., Application of expfunction method for nonlinear evolution equations with variable coefficients, Phys. Lett., A 369 (2007), 62-69. doi: 10.1016/j.physleta.2007.04.075
   Web of Science ®Google Scholar
• Kudryashov, N.A., Loguinova, N.B., Extended simplest equation method for nonlinear differential equations, Appl. Math. Comput., 205 (2008), 396-402.
   Web of Science ®Google Scholar
• Kudryashov, N.A., Exact solutions of generalized Kuramoto. Sivashinsky equation, Phys. Lett. A, 147 (1990), 287-291. doi: 10.1016/0375-9601(90)90449-X
   Web of Science ®Google Scholar
• Liu, S., Fu, Z., Liu, S., Zhao, Q., Jacobi elliptic function expansion method and periodic wave solutions of non linear wave equations, Phys. Lett.,A 289 (2001), 69-74. doi: 10.1016/S0375-9601(01)00580-1
   Web of Science ®Google Scholar
• Lu, D., Shi, Q., New Jacobi elliptic functions solutions for the combined KdV-mKdV equation, Int. J. Nonlinear Sci., 10 (2010), 320325.
   Google Scholar
• Parkes, E.J., Duffy, B.R., An automated tansh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys.Comm., 698 (2005), 288-300.
   Google Scholar
• A.H. Salas, “Exact solutions of coupled sine-Gordon equations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3930– 3935, 2010. doi: 10.1016/j.nonrwa.2010.02.020
   Web of Science ®Google Scholar
• Y.-M. Zhao, H. Liu, and Y.-J. Yang, “Applications of the Jacobi elliptic function expansion method for obtaining travelling wave solutions of coupled sine-Gordon equations,” Mathematical Sciences Research Journal, vol. 15, no. 3, pp. 80–90, 2011.
   Google Scholar
• Y.-M. Zhao, H. Liu, and Y.-J. Yang, “Exact solutions for the coupled Sine-Gordon equations by a new hyperbolic auxiliary function method,” Applied Mathematical Sciences, vol. 5, no. 33-36, pp. 1621– 1629, 2011.
   Google Scholar
• Y.-M. Zhao, W. Li, and Y.-J. Yang, “New exact solutions of coupled sine-Gordon equations using symbolic computation,” Mathematical Sciences Research Journal, vol. 14, no. 4, pp. 79– 86, 2010.
   Google Scholar
• A Neirameh, New analytical solutions for the coupled nonlinear Maccari’s system Alexandria Engineering Journal 55 (3), 2839-2847. doi: 10.1016/j.aej.2016.07.007
   Web of Science ®Google Scholar
• M Mehdipoor, A Neirameh, New soliton solutions to the (3+ 1)-dimensional Jimbo–Miwa equation, Optik 126 (23), 4718-4722. doi: 10.1016/j.ijleo.2015.08.019
   Web of Science ®Google Scholar
• H Rezazadeh, A Neirameh, M Eslami, A Bekir, A Korkmaz, A subequation method for solving the cubic–quartic NLSE with the Kerr law nonlinearity, Modern Physics Letters B 33 (18), 1950197. doi: 10.1142/S0217984919501975
   Web of Science ®Google Scholar
• A Neirameh, Topological soliton solutions to the coupled Schrodinger– Boussinesq equation by the SEM, Optik 126 (23), 4179-4183. doi: 10.1016/j.ijleo.2015.08.028
   Web of Science ®Google Scholar
• A Kurt, H Rezazadeh, M Senol, A Neirameh, O Tasbozan, M Eslami, Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves, Journal of Ocean Engineering and Science 4 (1), 24-32. doi: 10.1016/j.joes.2018.12.004
   Web of Science ®Google Scholar
• B. Ghanbari, M. Inc. A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation, Eur. Phys. J. Plus., (2018), 133, 1-19. doi: 10.1140/epjp/i2018-11984-1
   Web of Science ®Google Scholar
• Ghanbari B, Kuo CK. Abundant wave solutions to two novel KP-like equations using an effective integration method. Physica Scripta. 2021 Feb 1; 96(4):045203. doi: 10.1088/1402-4896/abde5a
   Web of Science ®Google Scholar
• Ghanbari B, Günerhan H, Ílhan OA, Baskonus HM. Some new families of exact solutions to a new extension of nonlinear Schrödinger equation. Physica Scripta. 2020 May 11; 95(7):075208. doi: 10.1088/1402-4896/ab8f42
   Web of Science ®Google Scholar
• Ghanbari B, Akgül A. Abundant new analytical and approximate solutions to the generalized Schamel equation. Physica Scripta. 2020 Apr 30; 95(7):075201. doi: 10.1088/1402-4896/ab8b27
   Web of Science ®Google Scholar
• Ahmad Neirameh, Solitary Wave Solutions to the Multidimensional Landau–Lifshitz Equation, Advances in Mathematical Physics, Volume 2021 |Article ID 5538516 | https://doi.org/10.1155/2021/5538516.
   Google Scholar