Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2008, Article ID 538489, 7 pages
http://dx.doi.org/10.1155/2008/538489
Research Article

Exp-Function Method for Solving Huxley Equation

Department of Mathematics, Kunming Teacher's College, Kunming, Yunnan 650031, China

Received 30 August 2007; Revised 13 January 2008; Accepted 24 January 2008

Academic Editor: Oleg Gendelman

Copyright © 2008 Xin-Wei Zhou. 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.

Linked References

  1. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” The Journal of Physiology, vol. 117, no. 4, pp. 500–544, 1952. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Wang, L. Q. Chen, and X. Y. Fei, “Bifurcation control of the Hodgkin-Huxley equations,” Chaos, Solitons & Fractals, vol. 33, no. 1, pp. 217–224, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. J. Wang, L. Chen, and X. Fei, “Analysis and control of the bifurcation of Hodgkin-Huxley model,” Chaos, Solitons & Fractals, vol. 31, no. 1, pp. 247–256, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-H. He, “A modified Hodgkin-Huxley model,” Chaos, Solitons & Fractals, vol. 29, no. 2, pp. 303–306, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J.-H. He and X.-H. Wu, “A modified Morris—Lecar model for interacting ion channels,” Neurocomputing, vol. 64, pp. 543–545, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J.-H. He, “Resistance in cell membrane and nerve fiber,” Neuroscience Letters, vol. 373, no. 1, pp. 48–50, 2005. View at Publisher · View at Google Scholar · View at PubMed
  7. L. X. Duan and Q. S. Lu, “Bursting oscillations near codimension-two bifurcations in the Chay Neuron model,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 59–64, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Q. Liu, T. Fan, and Q. S. Lu, “The spike order of the winnerless competition (WLC) model and its application to the inhibition neural system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 133–138, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. J. Zhang, J. X. Xu, H. Yao, and R.-X. Wei, “Mechanism of bifurcation-dependent coherence resonance of an excitable neuron model,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 4, pp. 447–450, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-H. He and X.-H. Wu, “Construction of solitary solution and compacton-like solution by variational iteration method,” Chaos, Solitons & Fractals, vol. 29, no. 1, pp. 108–113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. B. Batiha, M. S. M. Noorani, and I. Hashim, “Numerical simulation of the generalized Huxley equation by He's variational iteration method,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 1322–1325, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J.-H. He, “Addendum: new interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. H. Hashemi, H. R. Mohammadi, Daniali, and D. D. Ganji, “Numerical simulation of the generalized Huxley equation by He's homotopy perturbation method,” Applied Mathematics and Computation, vol. 192, no. 1, pp. 157–161, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. A.-M. Wazwaz and A. Gorguis, “An analytic study of Fisher's equation by using Adomian decomposition method,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 609–620, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Abdul-Majid Wazwaz, “Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 754–761, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J.-L. Zhang, M.-L. Wang, and X.-R. Li, “The subsidiary elliptic-like equation and the exact solutions of the higher-order nonlinear Schrödinger equation,” Chaos, Solitons & Fractals, vol. 33, no. 5, pp. 1450–1457, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. C. Dai, G. Zhou, and J. Zhang, “Exotic localized structures based on variable separation solution of (2+1)-dimensional KdV equation via the extended tanh-function method,” Chaos, Solitons & Fractals, vol. 33, no. 5, pp. 1458–1467, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. Ghorbani and J. Saberi-Nadjafi, “He's homotopy perturbation method for calculating Adomian polynomials,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 229–232, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Q. K. Ghori, M. Ahmed, and A. M. Siddiqui, “Application of homotopy perturbation method to squeezing flow of a Newtonian fluid,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 179–184, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. A. Rana, A. M. Siddiqui, Q. K. Ghori et al., “Application of He's homotopy perturbation method to Sumudu transform,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 185–190, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. E. Yusufoglu, “Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 153–158, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. H. Tari, D. D. Ganji, and M. Rostamian, “Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 2, pp. 203–210, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. X.-H. Wu and J.-H. He, “Solitary solutions, periodic solutions and compacton-like solutions using the exp-function method,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 966–986, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J.H. He and L.N. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent–Miodek equations using the Exp-function method,” Physics Letters A, vol. 372, no. 7, pp. 1044–1047, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J.-H. He and M. A. Abdou, “New periodic solutions for nonlinear evolution equations using Exp-function method,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1421–1429, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. S.-D. Zhu, “Exp-function method for the hybrid-lattice system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 461–464, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. S.-D. Zhu, “Exp-function method for the discrete mKdV lattice,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 465–468, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. J.-H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation. de-Verlag im Internet GmbH, Berlin, Germany, 2006. View at Zentralblatt MATH · View at MathSciNet
  31. R. K. Bullough and P. J. Caudre, Eds., Solitons, R. K. Bullough and P. J. Caudre, Eds., vol. 17 of Topics in Current Physics, Springer, Berlin, Germany, 1980. View at Zentralblatt MATH · View at MathSciNet
  32. F. Lambert and M. Musette, “Solitary waves, padeons and solitons,” in Padé Approximation and Its Applications Bad Honnef 1983, vol. 1071 of Lecture Notes in Mathematics, pp. 197–212, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. X.-H. Wu and J.-H. He, “Solitary solutions, periodic solutions and compacton-like solutions using the exp-function method,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 966–986, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. A. Bekir and A. Boz, “Exact solutions for a class of nonlinear partial differential equations using exp-function method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 4, pp. 505–512, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet