University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations

Rossides, T, Lloyd, DJB and Zelik, S (2015) Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations JOURNAL OF SCIENTIFIC COMPUTING, 63 (3). pp. 799-819.

[img]
Preview
Text (licence)
SRI_deposit_agreement.pdf
Available under License : See the attached licence file.

Download (33kB) | Preview
[img]
Preview
Text
RGL_multi_fronts.pdf
Available under License : See the attached licence file.

Download (1MB) | Preview

Abstract

We develop an efficient and robust numerical scheme to compute multi-fronts in one-dimensional real Ginzburg–Landau equations that range from well-separated to strongly interacting and colliding. The scheme is based on the global centre-manifold reduction where one considers an initial sum of fronts plus a remainder function (not necessarily small) and applying a suitable projection based on the neutral eigenmodes of each front. Such a scheme efficiently captures the weakly interacting tails of the fronts. Furthermore, as the fronts become strongly interacting, we show how they may be added to the remainder function to accurately compute through collisions. We then present results of our numerical scheme applied to various real Ginzburg Landau equations where we observe colliding fronts, travelling fronts and fronts converging to bound states. Finally, we discuss how this numerical scheme can be extended to general PDE systems and other multi-localised structures.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Computing Science
Authors :
AuthorsEmailORCID
Rossides, TUNSPECIFIEDUNSPECIFIED
Lloyd, DJBUNSPECIFIEDUNSPECIFIED
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 1 June 2015
Identification Number : 10.1007/s10915-014-9917-y
Uncontrolled Keywords : Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Numerical scheme, Computing localised states, Fronts interaction, Real Ginzburg Landau equation, Projection method, DYNAMICS, EXISTENCE, PULSES
Related URLs :
Additional Information : The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9917-y
Depositing User : Symplectic Elements
Date Deposited : 24 Jun 2015 17:15
Last Modified : 01 Jun 2016 01:08
URI: http://epubs.surrey.ac.uk/id/eprint/807867

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800