Kinks in stripe forming systems under traveling wave forcing

Previous Article
Comparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain
DCDS-B Home
This Issue
Next Article
Asymptotic speed of spread and traveling waves for a nonlocal epidemic model

November 2005, 5(4): 1027-1042. doi: 10.3934/dcdsb.2005.5.1027

Kinks in stripe forming systems under traveling wave forcing

S. Rüdiger ^1, , J. Casademunt ^2, and L. Kramer ^3,

1.	Hahn-Meitner Institut, Glienicker Str. 100, 14109 Berlin, Germany
2.	Facultat de Física, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona, Spain
3.	Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany

Received October 2004 Revised April 2005 Published August 2005

Abstract
Related Papers

We study domain walls in stripe forming systems that are externally forced by a periodic pattern, which is close to spatial resonance of 2:1 (the period of the forcing being half of the internal wavelength) and moving relative to the internal pattern. Two transitions are identified: A transition where the pattern lags behind the forcing as the forcing becomes too fast and a spontaneous symmetry-breaking transition of walls (kinks). The departure from perfect resonance is found to render the kink bifurcation imperfect and causes the walls to drift. We study the velocity of the kinks, which behaves strongly nonlinear close to the transitions. A phase approximation is used to understand the behavior and is found to be valid in a large range of parameters. Results from the phase equation can be generalized to hold for different ratios n:1.

Keywords: solitons, perturbations., Bifurcation.

Mathematics Subject Classification: Primary: 58J55, 35Q51; Secondary: 35B2.

Citation: S. Rüdiger, J. Casademunt, L. Kramer. Kinks in stripe forming systems under traveling wave forcing. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1027-1042. doi: 10.3934/dcdsb.2005.5.1027

[1]	Emile Franc Doungmo Goufo, Melusi Khumalo, Patrick M. Tchepmo Djomegni. Perturbations of Hindmarsh-Rose neuron dynamics by fractional operators: Bifurcation, firing and chaotic bursts. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 663-682. doi: 10.3934/dcdss.2020036
[2]	Vieri Benci, Donato Fortunato. Hylomorphic solitons on lattices. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 875-897. doi: 10.3934/dcds.2010.28.875
[3]	Adrian Constantin. Solitons from the Lagrangian perspective. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 469-481. doi: 10.3934/dcds.2007.19.469
[4]	Vieri Benci. Solitons and Bohmian mechanics. Discrete & Continuous Dynamical Systems - A, 2002, 8 (2) : 303-317. doi: 10.3934/dcds.2002.8.303
[5]	Isabel Mercader, Oriol Batiste, Arantxa Alonso, Edgar Knobloch. Dissipative solitons in binary fluid convection. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1213-1225. doi: 10.3934/dcdss.2011.4.1213
[6]	S. Raynor, G. Staffilani. Low regularity stability of solitons for the KDV equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 277-296. doi: 10.3934/cpaa.2003.2.277
[7]	Yvan Martel, Frank Merle. Inelastic interaction of nearly equal solitons for the BBM equation. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 487-532. doi: 10.3934/dcds.2010.27.487
[8]	Yvan Martel, Frank Merle. Refined asymptotics around solitons for gKdV equations. Discrete & Continuous Dynamical Systems - A, 2008, 20 (2) : 177-218. doi: 10.3934/dcds.2008.20.177
[9]	David M. A. Stuart. Solitons on pseudo-Riemannian manifolds: stability and motion. Electronic Research Announcements, 2000, 6: 75-89.
[10]	V. S. Gerdjikov, A. V. Kyuldjiev, M. D. Todorov. Manakov solitons and effects of external potential wells. Conference Publications, 2015, 2015 (special) : 505-514. doi: 10.3934/proc.2015.0505
[11]	Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1063-1079. doi: 10.3934/cpaa.2012.11.1063
[12]	Said Hadd, Rosanna Manzo, Abdelaziz Rhandi. Unbounded perturbations of the generator domain. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 703-723. doi: 10.3934/dcds.2015.35.703
[13]	Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control & Related Fields, 2018, 8 (2) : 397-410. doi: 10.3934/mcrf.2018016
[14]	Mohamed Sami ElBialy. Locally Lipschitz perturbations of bisemigroups. Communications on Pure & Applied Analysis, 2010, 9 (2) : 327-349. doi: 10.3934/cpaa.2010.9.327
[15]	Alfonso Artigue. Lipschitz perturbations of expansive systems. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 1829-1841. doi: 10.3934/dcds.2015.35.1829
[16]	Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. Perturbations of nonlinear eigenvalue problems. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1403-1431. doi: 10.3934/cpaa.2019068
[17]	Christian Lax, Sebastian Walcher. Singular perturbations and scaling. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-29. doi: 10.3934/dcdsb.2019170
[18]	Patrick M. Fitzpatrick, Jacobo Pejsachowicz. Branching and bifurcation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1955-1975. doi: 10.3934/dcdss.2019127
[19]	P.G. Kevrekidis, Dimitri J. Frantzeskakis. Multiple dark solitons in Bose-Einstein condensates at finite temperatures. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1199-1212. doi: 10.3934/dcdss.2011.4.1199
[20]	Francisco J. Diaz-Otero, Pedro Chamorro-Posada. Interaction length of DM solitons in the presence of third order dispersion with loss and amplification. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1069-1078. doi: 10.3934/dcdss.2011.4.1069

2018 Impact Factor: 1.008

American Institute of Mathematical Sciences