Regularizing the Cross-Newell equation by re-modulating along a characteristic angle
Analysis of PDEs
2020-04-16 v1
Abstract
A regularization of the Cross-Newell equation is presented. It is based on a secondary re-modulation along characteristics. This new characteristic Cross-Newell equation is not isotropic (has preferred directions), but is universal (homogeneous in and equation independent coefficients), has fourth derivatives, and generates localized solutions that are bi-asymptotic to rolls. Re-modulation of rolls in the Ginzburg-Landau equation is used for illustration of the theory.
Cite
@article{arxiv.2004.06944,
title = {Regularizing the Cross-Newell equation by re-modulating along a characteristic angle},
author = {Nicholas J Burgess and Thomas J Bridges},
journal= {arXiv preprint arXiv:2004.06944},
year = {2020}
}
Comments
15 pages, 1 figure