Traveling Wave Solutions for Bistable Diierential-diierence Equations with Periodic Diiusion Draft Version
نویسنده
چکیده
We consider traveling wave solutions to spatially discrete reaction-diiusion equations with nonlocal variable diiusion and bistable nonlinearities. For the case of spatially periodic diiusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly deened in the general periodic case and we provide an explicit formula for the case of period two diiusion. We present numerical results for the the cases of homogeneous, period two, and period four diiusion coeecients using a cubic nonlinearity, and uncover, numerically, a period doubling bifurcation in the wave speed versus detuning parameter relation.
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Analysis and Computation of Traveling Wave Solutions of Bistable Differential-difference Equations
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