Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu


Solitons Solutions of the Complex Ginzburg-Landau Equation with Saturation Term Using Painleve Truncated Approach

Journal of Applied Nonlinear Dynamics 10(2) (2021) 279--286 | DOI:10.5890/JAND.2021.06.007

P.H. Kamdoum-Tamo$^{1,2}$ , A. Kenfack-Jiotsa$^{1,2}$, T.C. Kofane$^{1}$

$^{1}$ Laboratory of Mechanics, Department of Physics, Faculty of Sciences, and African Center of Excellence in I.C.T ( C.E.T.I.C ) University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

$^{2}$ Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers' Training College, University of Yaounde I, P.O. Box 47 Yaounde, Cameroon

Download Full Text PDF

 

Abstract

Considering the pulse ansatz, we derive different classes of the modified complex Ginzburg-Landau (MCGL) equation and we use the Painleve truncated approach to construct the solitons solutions . We then present the importance of the saturation term. The solutions obtained by the combined methods are asymmetric- dark and bright solitons. Numerical simulations are performed to show how the wave propagates. The shape of solutions can be well controlled by adjusting the parameters of the system.

References

  1. [1]  Cheng, J.B. and Geng, X.G. (2005), Algebro-geometric solution to the modified Kadomtsev-Petviashvili equation, ph{J. Phys. Soc. Japan}, 74, 2217-2222.
  2. [2]  Geng, X.G., Dai, H.H., and Cao, C.W. (2003), Algebro-geometric constructions of the discrete Ablowitz-Ladik flow and applications, ph{J. Math. Phys.}, 44, 4573-4588.
  3. [3]  Lou, S.Y., Tang, X.Y., and Lin, J. (2001), Exact solutions of the coupled KdV system via formally variable separation approach, ph{Commun. Theor. Phys.}, 36, 145-148.
  4. [4]  Zhang, S.L., Lou, S.Y., and Qu, C.Z. (2006), The derivative-dependent functional variable separation for the solving equations, ph{Chin. Phys.}, 15, 2765-2776.
  5. [5]  Kengne, E., Vaillancour, R., and Malomed, B.A. (2006), Coupled nonlinear Schr\"{o}dinger equationa for solitary-wave kink signals propagating in discrete nonlinear dispersive transmission lines, ph{Int. J. of Modern Phy. B.}, 23, 133-147.
  6. [6]  Li, D.S. and Zhang, H.Q. (2004), A new extended tanh-function method and its application to the dispersive long wave equations in (2+1) dimensions, ph{Appl. Math. Comput.}, 147, 789-797.
  7. [7]  Bekir, A. (2008), New solitons and periodic wave solutions for some nonlinear physical models by using the sine-cosine method, ph{Phys. Scr.}, 77, 501-505.
  8. [8]  Mehdi, D. and Fatemeh, S. (2007), Solution of a partial differential equation subject to temperature overspecification by Hes homotopy perturbation method, ph{Phys. Scr.}, 75, 778-787.
  9. [9]  Hirota, R. (1971), Exact solution of the Korteweg-de-Vries equation for multiple collisions of solitons, ph{Phys. Rev. Lett.}, 27, 1192-1194.
  10. [10]  Zayed, E.M.E. and Abdelaziz, M.A.M. (2011), Exact solutions for the nonlinear Schr\"{o}dinger equation with variabe coefficients using the generalized extended tanh-function, the sine-cosine and the exp-function methods, ph{Appl. Math. Comput.}, 218, 2259-2268.
  11. [11]  Kudryashov, N.A. (2012), One method for finding exact solutions of nonlinear differential equations, ph{commun. Nonlinear Sci. Numer. Simulat.}, 17, 2248-2253.
  12. [12]  Zayed, E.M.E., Moatimid, G.M., and Al-Nowehy Abdul-Ghani A.A. (2015), The generalized Kudryashov method andits applicationsfor solving nonlinear PDEs in mathematical physics, ph{Scientific J. Math. Res.}, 5, 19-39.
  13. [13]  Moatimid, G.M., El-Shiekh Rehad, M., and Al-Nowehy Abdul-Ghani A.A. (2013), Exact solutions for Calegero-Bogoyavlenskii-Schiff equation using symmetry mthod, ph{Appl. Math. comput.}, 220, 455-462.
  14. [14]  Moussa, M.H.M. and El-Schiek Rehab, M. (2006), Similarity reduction and similarity solutions of Zabolotskay-Khoklov equatio with a dissipative term via symmetry method, ph{Physica A}, 371, 325-335.
  15. [15]  Biswas, A., Milovic, D., and Edwards, M. (2010), ph{Mathematical Theory of Dispersion-Managed Optical Solitons}, Springer-Verlag, New York.
  16. [16]  Sarma, A.K., Saha, M., and Biswas, A. (2010), Optical solitons with power law nonlinearity and hamiltonian perturbation: an exact solution, ph{J. Infrared Milli. Terahertz Waves}, 31, 1048-1056.
  17. [17]  Tsigaridas, G., Fragos, A., Polyzos, I., Fakis, M., Ioannou, A., Giannetas, V., and Persephonis, P. (2005), Evolution of near-soliton initial conditions in non-linear wave equations through their B\"{a}cklund transforms, ph{Chaos Solitons Fract.}, 23, 1841-1854.
  18. [18]  Wang, M., Li, X., and Zhang, J. (2008), The $(G/G)$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, ph{Phys. Lett. A}, 372, 417-423.
  19. [19]  Vakhnenko, V.O., Parkes, E.J., and Morrison, A.J. (2003), A B\"{a}cklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, ph{chaos solitons Fractals}, 17, 683-692.
  20. [20]  Mohamadou, A., Ndzana II, F., and Kofan\{e}, T.C. (2006), Pulse solution of the modified cubic complex Ginzburg-Landau equation, ph{Phys. Scr.}, 73, 596-600.
  21. [21]  Yomba, E. and Kofan\{e} T.C. (1996), On exact solutions of the generalized modified complex Ginzburg-Landau equation using the Weiss-Tabor-Carnevale method, ph{Phys. Scr.}, 54, 576-580.
  22. [22]  Yomba, E. and Kofan\{e} T.C. (1999), On exact solutions of the modified complex Ginzburg-Landau equation, ph{Physica D}, 125, 105-122.