Table of Contents
International Journal of Engineering Mathematics
Volume 2015, Article ID 107978, 35 pages
http://dx.doi.org/10.1155/2015/107978
Research Article

New Improvement of the Expansion Methods for Solving the Generalized Fitzhugh-Nagumo Equation with Time-Dependent Coefficients

Department of Applied Mathematics, Faculty of Mathematics Science, University of Tabriz, Tabriz 51569 84687, Iran

Received 30 May 2015; Revised 10 September 2015; Accepted 10 September 2015

Academic Editor: Josè A. Tenereiro Machado

Copyright © 2015 Jalil Manafian and Mehrdad Lakestani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [27 citations]

The following is the list of published articles that have cited the current article.

  • Syed Tauseef Mohyud-Din, and Amna Irshad, “On exact solutions of modified KdV-ZK equation,” Alexandria Engineering Journal, 2016. View at Publisher · View at Google Scholar
  • Mehdi Fazli Aghdaei, and Jalil Manafian, “Optical soliton wave solutions to the resonant Davey–Stewartson system,” Optical and Quantum Electronics, vol. 48, no. 8, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, Mehdi Fazli Aghdaei, and Manouchehr Zadahmad, “Analytic study of sixth-order thin-film equation by tan(ϕ/2)-expansion method,” Optical and Quantum Electronics, vol. 48, no. 8, 2016. View at Publisher · View at Google Scholar
  • Haci Mehmet Baskonus, and Hasan Bulut, “New wave behaviors of the system of equations for the ion sound and Langmuir Waves,” Waves in Random and Complex Media, pp. 1–13, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, and Mehdi Fazli Aghdaei, “Abundant soliton solutions for the coupled Schrödinger-Boussinesq system via an analytical method,” The European Physical Journal Plus, vol. 131, no. 4, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, and Mehrdad Lakestani, “Abundant soliton solutions for the Kundu–Eckhaus equation via tan(ϕ(ξ))-expansion method,” Optik - International Journal for Light and Electron Optics, 2016. View at Publisher · View at Google Scholar
  • Qin Zhou, M. Ekici, A. Sonmezoglu, J. Manafian, S. Khaleghizadeh, and M. Mirzazadeh, “Exact solitary wave solutions to the generalized Fisher equation,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 24, pp. 12085–12092, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, and Mehrdad Lakestani, “Optical soliton solutions for the Gerdjikov–Ivanov model via tan(ϕ/2)-expansion method,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 20, pp. 9603–9620, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, and Mehrdad Lakestani, “Dispersive dark optical soliton with Tzitzéica type nonlinear evolution equations arising in nonlinear optics,” Optical and Quantum Electronics, vol. 48, no. 2, 2016. View at Publisher · View at Google Scholar
  • Jalil Manafian, Peyman Bolghar, and Atefeh Mohammadalian, “Abundant soliton solutions of the resonant nonlinear Schrödinger equation with time-dependent coefficients by ITEM and He’s semi-inverse method,” Optical and Quantum Electronics, vol. 49, no. 10, 2017. View at Publisher · View at Google Scholar
  • K. Hosseini, Z. Ayati, and R. Ansari, “New exact solutions of the Tzitzéica type equations arising in nonlinear optics using a modified version of the improved $$\tan \left( {\varPhi \left( \xi \right)/2} \right)$$ tan Φ ξ / 2 -expansion method,” Optical and Quantum Electronics, vol. 49, no. 8, 2017. View at Publisher · View at Google Scholar
  • Mehdi Fazli Aghdaei, “Kerr-law nonlinearity of the resonant nonlinear Schrodinger?s equation with time-dependent coefficients,” Optical and Quantum Electronics, vol. 49, no. 7, 2017. View at Publisher · View at Google Scholar
  • Jalil Manafian, Mehdi Fazli Aghdaei, Morteza Khalilian, and Ramin Sarbaz Jeddi, “Application of the generalized G′/G-expansion method for nonlinear PDEs to obtaining soliton wave solution,” Optik - International Journal for Light and Electron Optics, vol. 135, pp. 395–406, 2017. View at Publisher · View at Google Scholar
  • Reza Farshbaf Zinati, and Jalil Manafian, “Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation,” The European Physical Journal Plus, vol. 132, no. 4, 2017. View at Publisher · View at Google Scholar
  • Mehrdad Lakestani, and Jalil Manafian, “Application of the ITEM for the modified dispersive water-wave system,” Optical and Quantum Electronics, vol. 49, no. 4, 2017. View at Publisher · View at Google Scholar
  • Cevat Teymuri Sindi, and Jalil Manafian, “Soliton solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas,” The European Physical Journal Plus, vol. 132, no. 2, 2017. View at Publisher · View at Google Scholar
  • Jalil Manafian, Jalal Jalali, and Arash Ranjbaran, “Applications of IBSOM and ETEM for solving a discrete electrical lattice,” Optical and Quantum Electronics, vol. 49, no. 12, 2017. View at Publisher · View at Google Scholar
  • D. Kumar, K. Hosseini, and F. Samadani, “The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics,” Optik - International Journal for Light and Electron Optics, vol. 149, pp. 439–446, 2017. View at Publisher · View at Google Scholar
  • Syed Tauseef Mohyud-Din, Amna Irshad, Naveed Ahmed, and Umar Khan, “Exact Solutions of (3+1)-dimensional generalized KP Equation Arising in Physics,” Results in Physics, 2017. View at Publisher · View at Google Scholar
  • Mohammadreza Foroutan, Isa Zamanpour, and Jalil Manafian, “Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions,” The European Physical Journal Plus, vol. 132, no. 10, 2017. View at Publisher · View at Google Scholar
  • Cevat Teymuri Sindi, and Jalil Manafian, “ Wave solutions for variants of the KdV-Burger and the K ( n , n )-Burger equations by the generalized G′/G-expansion method ,” Mathematical Methods in the Applied Sciences, 2017. View at Publisher · View at Google Scholar
  • Jalil Manafian, and Reza Farshbaf Zinati, “Application of $$\tan (\Phi (\xi )/2)$$tan(Φ(ξ)/2)-expansion method to solve some nonlinear fractional physical model,” Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2018. View at Publisher · View at Google Scholar
  • Umar Khan, Amna Irshad, Naveed Ahmed, and Syed Tauseef Mohyud-Din, “Improved tan$$\left( {\frac{{\phi \left(\varvec{\xi}\right)}}{2}} \right)$$ϕξ2-expansion method for (2 + 1)-dimensional KP–BBM wave equation,” Optical and Quantum Electronics, vol. 50, no. 3, 2018. View at Publisher · View at Google Scholar
  • Cevat Teymuri Sendi, Jalil Manafian, Hasan Mobasseri, Mohammad Mirzazadeh, Qin Zhou, and Ahmet Bekir, “Application of the ITEM for solving three nonlinear evolution equations arising in fluid mechanics,” Nonlinear Dynamics, 2018. View at Publisher · View at Google Scholar
  • Naveed Ahmed, Amna Irshad, Syed Tauseef Mohyud-Din, and Umar Khan, “Exact solutions of perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by improved $${\textbf{tan}} \left( {\frac{{\boldsymbol{\phi}} \left( {\boldsymbol{\xi}} \right)}{{\textbf{2}}}} \right)$$tanϕξ2-expansion method,” Optical and Quantum Electronics, vol. 50, no. 1, 2018. View at Publisher · View at Google Scholar
  • P. Agarwal, S. Deni̇z, S. Jain, A.A. Alderremy, and Shaban Aly, “A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques,” Physica A: Statistical Mechanics and its Applications, pp. 122769, 2019. View at Publisher · View at Google Scholar
  • Henk Koppelaar, Parastou Kordestani Moghadam, Kamruzzaman Khan, Sareh Kouhkani, Gijs Segers, and Martin van Warmerdam, “Reaction Time Improvements by Neural Bistability,” Behavioral Sciences, vol. 9, no. 3, pp. 28, 2019. View at Publisher · View at Google Scholar