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Traveling wave solutions to modified Burgers and diffusionless Fisher PDE's

  • Corresponding author: Kale Oyedeji, 470-639-0285

    Corresponding author: Kale Oyedeji, 470-639-0285
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  • We investigate traveling wave (TW) solutions to modified versionsof the Burgers and Fisher PDE’s. Both equations are nonlinear parabolicPDE’s having square-root dynamics in their advection and reaction terms.Under certain assumptions, exact forms are constructed for the TW solutions.

    Mathematics Subject Classification: Primary: 34E05, 35K57; Secondary: 35B09, 35B40.

    Citation:

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  • Figure 1.  a) $ v(z) $ vs $ z $, b) $ f(z) = v(z)^2 $ vs $ z $. See Eqs. (5.10) and (5.13).

    Figure 2.  a) $ v(z) $ vs $ z $, \quad b) $ f(z) $ vs $ z $. See Eq. (5.15).

  • [1] R. Buckmire, K. McMurtry and R. E. Mickens, Numerical studies of a nonlinear heat equation with square root reaction term, Numerical Methods for Partial Differential Equations, 25 (2009), 598-609. doi: 10.1002/num.20361.
    [2] L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhäuser, Boston, 1997.
    [3] P. M. Jordan, Finite-amplitude acoustic traveling waves in a fluid that saturates a porous media, Physics Letters A, 355 (2006), 216-221.
    [4] P. M. Jordan, A Note on the Lambert W-function: Applications in the mathematical and physical sciences, Contemporary Mathematics, 618 (2014), 247-263. doi: 10.1090/conm/618/12351.
    [5] J. D. Logan, Nonlinear Partial Differential Equations Wiley-Interscience, New York, 1994.
    [6] R. E. Mickens, Exact finite difference scheme for an advection equation having square-root dynamics, Journal of Difference Equations and Applications, 14 (2008), 1149-1157. doi: 10.1080/10236190802332209.
    [7] R. E. Mickens, Wave front behavior of traveling waves solutions for a PDE having square-root dynamics, Mathematics and Computers in Simulation, 82 (2012), 1271-1277. doi: 10.1016/j.matcom.2010.08.010.
    [8] R. E. Mickens, Mathematical Methods for the Natural and Engineering Sciences, 2nd edition, World Scientific, London, 2017.
    [9] J. D. Murray, Mathematical Biology, Springer, Berlin, 1993. doi: 10.1007/b98869.
    [10] S. I. Soluyan and R. V. Khokhlov, Finite amplitude acoustic waves in a relaxing medium, Soviet Physics - Acoustic, 8 (1962), 170-175.
    [11] S. R. Valluri, D. J. Jeffrey and R. M. Corless, Some applications of the Lambert W function to physics, Canadian Journal of Physics, 78 (2000), 823-831.
    [12] G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974.
    [13] H. Wilhelmsson, M. Benda, B. Etlicher, R. Jancel and T. Lehner, Non-linear evolution of densities in the presence of simultaneous diffusion and reaction processes, Physica Scripta, 38 (1988), 1482-1489. doi: 10.1103/PhysRevA.38.1482.
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