Kessler, David A.Levine, Herbert2017-05-222017-05-222016Kessler, David A. and Levine, Herbert. "Nonlinear self-adapting wave patterns." <i>New Journal of Physics,</i> 18, (2016) IOP Publishing: https://doi.org/10.1088/1367-2630/18/12/122001.https://hdl.handle.net/1911/94314We propose a new type of traveling wave pattern, one that can adapt to the size of physical system in which it is embedded. Such a system arises when the initial state has an instability for a range of wavevectors, k, that extends down to k = 0, connecting at that point to two symmetry modes of the underlying dynamical system. The Min system of proteins in E. coli is such a system with the symmetry emerging from the global conservation of two proteins, MinD and MinE. For this and related systems, traveling waves can adiabatically deform as the system is increased in size without the increase in node number that would be expected for an oscillatory version of a Turing instability containing an allowed wavenumber band with a finite minimum.engOriginal content from this work may be used under the terms of theﾠCreative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Journal articlehttps://doi.org/10.1088/1367-2630/18/12/122001