Regularizing the Cross-Newell equation by re-modulating along a characteristic angle

2020/04/15 by Nicholas J Burgess, Burgess, Nicholas J, Thomas J. Bridges +1
Computer Science · Mathematics · #35B36 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2004.06944

openalex publication_date 2020/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

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