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New exact solutions to the Fitzhugh-Nagumo equation. (English) Zbl 1102.35315

Summary: By the first integral method, a series of new exact solutions of the Fitzhugh-Nagumo equation have been obtained. It is shown that this method is one of the most effective approaches to obtain the exact solutions of the nonlinear evolution equations, especially for nonintegrable models.

MSC:

35C05 Solutions to PDEs in closed form
35K57 Reaction-diffusion equations
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[1] Fitzhugh, R., Impulse and physiological states in models of nerve membrane, Biophys. J., 1, 445-466 (1961)
[2] Nagumo, J. S.; Arimoto, S.; Yoshizawa, S., An active pulse transmission line simulating nerve axon, Proc. IRE, 50, 2061-2070 (1962)
[3] Aronson, D. G.; Weinberger, H. F., Multidimensional nonlinear diffusion arising in population genetics, Adv. Math., 30, 33-76 (1978) · Zbl 0407.92014
[4] Kawahara, T.; Tanaka, M., Interaction of travelling fronts: an exact solution of a nonlinear diffusion equation, Phys. Lett. A, 97, 311-314 (1983)
[5] Nucci, M. C.; Clarkson, P. A., The nonclassical method is more general than the direct method for symmetry reductions: an example of the Fitzhugh-Nagumo equation, Phys. Lett. A, 164, 49-56 (1992)
[6] Chen, D. Y.; Gu, Y., Cole-Hopf quotient and exact solutions of the generalized Fitzhugh-Nagumo equations, Acta Math. Sci., 19, 1, 7-14 (1999) · Zbl 0922.35032
[7] Shih, M.; Momoniat, E.; Mahomed, F. M., Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh-Nagumo equation, J. Math. Phys., 46, 023503 (2005) · Zbl 1076.35052
[8] Feng, Z. S., On explicit exact solutions to the compound Burgers-KdV equation, Phys. Lett. A, 293, 57-66 (2002) · Zbl 0984.35138
[9] Feng, Z. S., The first-integral method to study the Burgers-Korteweg-de Vries equation, J. Phys. A: Math. Gen., 35, 343-349 (2002) · Zbl 1040.35096
[10] Feng, Z. S., Exact solution to an approximate sine-Gordon equation in \((n+1)\)-dimensional space, Phys. Lett. A, 302, 64-76 (2002) · Zbl 0998.35046
[11] Feng, Z. S.; Wang, X. H., The first integral method to the two-dimensional Burgers-Korteweg-de Vries equation, Phys. Lett. A, 308, 173-178 (2003) · Zbl 1008.35062
[12] Naranmandula; Wang, K. X., New explicit exact solutions to a nonlinear dispersive-dissipative equation, Chin. Phys., 13, 2, 139-143 (2004)
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