English

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 \eps\eps 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.

Keywords

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

R2 v1 2026-06-23T14:51:53.522Z