References
- Murray, J., Mathematical Biology, Second Edition. Springer, Berlin, 1993.
- Kapral, R. and Showalter, K. (Eds), Chemical waves and Patterns, Kluwer, Doordrecht (1995).
- Volpert, A. I. and Volpert, V. A., Traveling waves solutions of parabolic systems, Transl. Math. Mono. Amer Math. Soc. Providence 140(1994).
- Field, R. J. and Burger, M., Oscillations and Traveling waves in Chemical Systems, J. Wiley, New York (1985).
- Evans, J. Nerve axon equations (iii). Stability of the never impulse., Indiana Univ. Math. J. 22(1972), 577-593.
- Evans, J. Nerve axon equations (iv). The stable and the unstable impulse., Indiana Univ. Math. J. 24(1975), 1169-1190.
- Gardner, R. A. and Jones C. K. R. T. Traveling waves of perturbed diffusion equation arising in a phase field model., India Univ. Math. J. 39(1990), 1197-1222. https://doi.org/10.1512/iumj.1990.39.39054
- Pego, R. and Weinstein, M. Eigenvalues and instability of solitary waves., Phil. Trans. R. Soc. Lond. A, 340(1992), 47-94. https://doi.org/10.1098/rsta.1992.0055
- Nii, S. Stability of traveling multiple-front (multiple-back) wave solution of the Fitzhugh-Nagumo equations., SIAM. J. Math. Anal. 28(1997), 1094-1112. https://doi.org/10.1137/S003614109528829X
- Afendikov, A. L. and Bridges, J. J. Instability of the Hocking-Stewartson pulse and its implications for three-dimensional, Proc. R. Soc. Lond. A. 457(2001), 257-272.
- Reddy, S. C. and Trefethen, L. N., Pseudo spectra of the convection diffusion operators., SIAM. Appl. Math. 54(1994), 1634-1649. https://doi.org/10.1137/S0036139993246982
- Alexander, J. C., Gardner, R. A. and Jones, C. K. R. T. A topological invariant arising in the stability analysis of traveling waves., J. Reine. Angew. Math. 410(1990), 167-212.
- Nii, S. A topological proof of stability of N-front solutions of the Fitzhugh-Nagumo equations., J. Dynam. Diff. Eqns. 11(1999), 515-555. https://doi.org/10.1023/A:1021965920761
- G. I. Sivashinsky, Acta. 4(1977), 1177.
- Y. Kuramoto and Tsuzuki. Theor. Phys. 55(1976), 356-369. https://doi.org/10.1143/PTP.55.356
- Y. Kuramoto and T. Yamada, Prog. Theo. Phys. 64 (1978), 346-367. https://doi.org/10.1143/PTPS.64.346
- Luwai Wazzan, A modified Tanh-Coth method for Solving the general Burgers-Fisher and The Kuramoto-Sivashinsky equations. Communications in Non Linear Science and Numerical Simulation, 14(2009), 2646-2652.
- John Weiss, M.Tobar and G. Carnevale, The Painleve' for Partial Differential Equations, J. Math. Phy. 24(1983), 552.
- Gui-qoing Xu, Zhi-bin Li, PDEP test: a package for the Painleve' test of nonlinear partial differential equations. Applied Mathematics and Computation, 169(2005), 1364-1379. https://doi.org/10.1016/j.amc.2004.10.055
- K. K. Victor, B. B. Thomas and T. C. Kofane, On the exact solution of the Schafer-Wayne short pulse equation: WKI eigenvalue problem. J. Phys. A, 39(2007), 5585.
- H. Sagan; Boundary and eigenvalue problems in mathematical physics, J. Wiley, (1989).
- P. Rosenau and J. M. Hyman, Phys. Rev. Lett. 70 (1993), 564. https://doi.org/10.1103/PhysRevLett.70.564
- P. Rosenau, Physica D, 123(1998), 525. https://doi.org/10.1016/S0167-2789(98)00148-1
- M. Tatari and M. Dehghan, On the convergence of He's variational iteration method, J. comp. Appl. Math., 207 (2007), 121-128. https://doi.org/10.1016/j.cam.2006.07.017
- He, J. H. Variational iteration method. Applied Mathematics and Computation., 114(1999), 699-708.
- W.H.Enright, Verifying approximate solutions to dierential equations, Comput. Appl. Math.,185(2006), 203-211. https://doi.org/10.1016/j.cam.2005.03.006
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