Abstract
We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.
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Guedda, M., Benlahsen, M. & Misbah, C. Exact steady states to a nonlinear surface growth model. Eur. Phys. J. B 83, 29 (2011). https://doi.org/10.1140/epjb/e2011-20403-8
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DOI: https://doi.org/10.1140/epjb/e2011-20403-8