Document Type : Original Article


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 Staße 9, Weimar, Germany


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.


[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.