Application of the F-Expansion Method for Solving the Fokas-Lenells Equation

Main Article Content

Ohoud A. Alshahrani


By the aid of traveling wave hypothesis, the F-expansion method has been implemented in this paper to obtain Jacobian-Elliptic function solutions for the optical Fokas-Lenells model. The hyperbolic-function solutions are derived as special cases from the Jacobian-Elliptic function solutions. The present approach is straightforward to determine the exact solutions for the Fokas-Lenells equation. The existence criteria of the obtained solutions are also reported.

Article Details


  1. A. Biswas, 1-Soliton solution of 1+2 dimensional nonlinear Schrödinger’s equation in power law media, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 1830–1833.
  2. A. Biswas, D. Milovic, Travelling wave solutions of the non-linear Schrödinger’s equation in non-Kerr law media, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 1993–1998.
  3. S.H. Crutcher, A.J. Osei, A. Biswas, Wobbling phenomena with logarithmic law nonlinear Schrödinger equations for incoherent spatial Gaussons, Optik. 124 (2013), 4793–4797.
  4. M. Eslami, M. Mirzazadeh, B. Fathi Vajargah, A. Biswas, Optical solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients by the first integral method, Optik. 125 (2014), 3107–3116.
  5. A.J. Mohamad Jawad, M.D. Petković, A. Biswas, Modified simple equation method for nonlinear evolution equations, Applied Mathematics and Computation. 217 (2010), 869–877.
  6. A.A. Gaber, A.F. Aljohani, A. Ebaid, J.T. Machado, The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type, Nonlinear Dyn. 95 (2019), 361–368.
  7. A.A. AlQarni, A. Ebaid, A.A. Alshaery, H.O. Bakodah, A. Biswas, S. Khan, M. Ekici, Q. Zhou, S.P. Moshokoa, M.R. Belic, Optical solitons for Lakshmanan–Porsezian–Daniel model by Riccati equation approach, Optik. 182 (2019), 922–929.
  8. Y.M. Mahrous, S.M. Khaled, A. Ebaid, An internet traffic flow model via a conformable derivative: The exact soliton solutions, Adv. Differ. Equ. Control Processes. 21 (2019), 227–237.
  9. D.A. Lott, A. Henriquez, B.J.M. Sturdevant, A. Biswas, A numerical study of optical soliton-like structures resulting from the nonlinear Schrödinger’s equation with square-root law nonlinearity, Appl. Math. Comput. 207 (2009), 319–326.
  10. M. Mirzazadeh, M. Eslami, B.F. Vajargah, A. Biswas, Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity, Optik. 125 (2014), 4246–4256.
  11. H.O. Bakodah, M.A. Banaja, B.A. Alrigi, A. Ebaid, R. Rach, An efficient modification of the decomposition method with a convergence parameter for solving Korteweg de Vries equations, J. King Saud Univ. - Sci. 31 (2019), 1424–1430.
  12. H. Triki, A.-M. Wazwaz, Combined optical solitary waves of the Fokas—Lenells equation, Waves Rand. Complex Media. 27 (2017), 587–593.
  13. H. Triki, A.-M. Wazwaz, New types of chirped soliton solutions for the Fokas–Lenells equation, Int. J. Numer. Methods Heat Fluid Flow. 27 (2017), 1596–1601.
  14. B. Salah, E.R. El-Zahar, A.F. Aljohani, A. Ebaid, M. Krid, Optical soliton solutions of the time-fractional perturbed Fokas-Lenells equation: Riemann-Liouville fractional derivative, Optik. 183 (2019), 1114–1119.
  15. A. Ebaid, E.R. El-Zahar, A.F. Aljohani, B. Salah, M. Krid, J.T. Machado, Exact solutions of the generalized nonlinear Fokas-Lennells equation, Results Phys. 14 (2019), 102472.
  16. A.J. Mohamad Jawad, A. Biswas, Q. Zhou, S.P. Moshokoa, M. Belic, Optical soliton perturbation of Fokas–Lenells equation with two integration schemes, Optik. 165 (2018), 111–116.
  17. A.F. Aljohani, E.R. El-Zahar, A. Ebaid, M. Ekici, A. Biswas, Optical soliton perturbation with Fokas-Lenells model by Riccati equation approach, Optik. 172 (2018), 741–745.
  18. A. Ebaid, E.H. Aly, Exact solutions for the transformed reduced Ostrovsky equation via the -expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions, Wave Motion. 49 (2012), 296–308.