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arXiv · 1003.3638

Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion

Alex Hansen·Bo-Sture Skagerstam·Glenn Tørå
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Abstract

We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to a balance between non-linear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations supports the view that anomalous diffusion and the solitary waves disclosed will be general features in such non-linear convective-diffusive dynamics.

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Alex Hansen, Bo-Sture Skagerstam, Glenn Tørå. 2011-02-27. Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion. https://doi.org/10.1103/physreve.83.056314

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