Document Type : Original Article

Authors

1 Department of Mathematics, Northwest University, Kano, Nigeria

2 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

3 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

4 Nord Sta&szlig;e 9, Weimar, Germany

Abstract

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE)that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutionsto the governing equation efficiently.

Keywords

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[1] Biswas, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S. P., & Belic, M. (2018). Optical solitons having weak non-local non-linearity by two integration schemes. Optik, 164, 380-384.
[2] Mirzazadeh, M., Eslami, M., & Biswas, A. (2014). Soliton solutions of the generalized Klein–Gordon equation by using (G′/G)-expansion method. Computational and Applied Mathematics, 33(3), 831-839.
[3] Rezazadeh, H. (2018). New solitons solutions of the complex Ginzburg-Landau equation with Kerr law non-linearity. Optik, 167,218-227.
[4] Rezazadeh, H., Mirhosseini-Alizamini, S. M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., & Abbagari, S. (2018). New optical solitons of non-linear conformable fractional Schrödinger-Hirota equation. Optik, 172, 545-553.
[5] Eslami, M., & Rezazadeh, H. (2016). The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo, 53(3), 475-485.
[6] Eslami, M., & Mirzazadeh, M. (2014). First integral method to look for exact solutions of a variety of Boussinesq-like equations. Ocean Engineering, 83, 133-137.
[7] Eslami, M., & Mirzazadeh, M. (2016). Optical solitons with Biswas–Milovic equation for power law and dual-power law non-linearities. Non-linear Dynamics, 83(1-2), 731-738.
[8] Eslami, M. (2016). Trial solution technique to chiral non-linear Schrodinger’s equation in (1+2)-dimensions. Non-linear Dynamics, 85(2), 813-816.
[9] Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., & Asghari, R.(2018). Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method. Optical and Quantum Electronics, 50(3), 150.
[10] Khodadad, F. S., Nazari, F., Eslami, M., & Rezazadeh, H. (2017).Soliton solutions of the conformable fractional Zakharov-Kuznetsov equation with dual-power law non-linearity. Optical and Quantum Electronics, 49(11), 384.
[11]Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., & Eslami, M. (2016). Optical solitons with Biswas–Milovic equation by extended trial equation method. Non-linear Dynamics, 84(4), 1883-1900.
[12] Jamilu S., Abdullahi J., & Abubakar M. G. (2018). New exact solutionfor the (3+1) conformable space–time fractional modified Korteweg–de-Vries equations via Sine-Cosine Method, Journal of Taibah University for Science, DOI:10.1080/16583655.2018.1537642,1-5.
[13]Lakhveer Kaura, Abdul-Majid Wazwaz, (2018). Optical solitons for perturbed GIE, Optik - International Journal for Light and Electron Optics 174, 447–451.
[14] Osman, M. S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). The Unified Method for Conformable Time Fractional Schrödinger Equation with Perturbation Terms. Chinese Journal of Physics, 56(5), 2500-2506.
[15] Korkmaz, A. (2017). Exact solutions to (3+ 1) conformable time fractional Jimbo–Miwa, Zakharov–Kuznetsov and modified Zakharov–Kuznetsov equations. Communications in Theoretical Physics, 67(5), 479.
[16] Korkmaz, A. (2018). On the wave solutions of conformable fractional evolution equations. Communications, 67, 68-79.
[17] Korkmaz, A., & Hosseini, K. (2017). Exact solutions of a non-linear conformable time-fractional parabolic equation with exponential non-linearity using reliable methods. Optical and Quantum Electronics, 49(8), 278.
[18] Korkmaz, A. (2018). Complex Wave Solutions to Mathematical Biology Models I: Newell–Whitehead–Segel and Zeldovich Equations. Journal of Computational and Non-linear Dynamics, 13(8), 081004.
[19] Fan, E. (2000). Integrable evolution systems based on GIEs, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation. Journal of Mathematical Physics, 41(11), 7769-7782.
[20] Dai, H. H., & Fan, E. G. (2004). Variable separation and algebro-geometric solutions of the GIE. Chaos, Solitons & Fractals, 22(1), 93-101.
[21] Manafian, J., & Lakestani, M. (2016). Optical soliton solutions for the Gerdjikov–Ivanov model via tan (ϕ/2)-expansion method. Optik-International Journal for Light and Electron Optics, 127(20), 9603-9620.
[22] Guo, L., Zhang, Y., Xu, S., Wu, Z., & He, J. (2014). The higher order rogue wave solutions of the GIE. Physica Scripta, 89(3), 035501.
[23] Kakei, S., & Kikuchi, T. (2005). Solutions of a derivative non-linear Schrödinger hierarchy and its similarity reduction. Glasgow Mathematical Journal, 47(A), 99-107.
[24] Xu, S., & He, J. (2012). The rogue wave and breather solution of the Gerdjikov-Ivanov equation. Journal of Mathematical Physics, 53(6), 063507.
[25] Sirendaoreji. (2006). A new auxiliary equation and exact travelling wave solutions of non-linear equations. Physics Letters A, 356(2), 124-130.