Abstract
Recent models motivated by biological phenomena lead to non-localPDEs or systems with singularities. It has been recently understood that these systems may havetraveling wave solutions that are not physically relevant[19].We present an original method that relies on the physical evolutionto capture the ``stable' traveling waves. This method allows us toobtain the traveling wave profiles and their traveling speedsimultaneously. It is easy to implement, and it applies to classicaldifferential equations as well as nonlocal equations and systemswith singularities. We also show the convergence of the schemeanalytically for bistable reaction diffusion equations over thewhole space $\mathbb{R}$.
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