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

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

2010-03-18

arxiv.org/abs/1003.3638v3

Physics

Condensed Matter

Soft Condensed Matter

Corrected typos, added 3 references and 2 figures

Scientific paper

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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