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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

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 and Continuous Dynamical Systems - B, 2005, 5 (4) : 1027-1042. doi: 10.3934/dcdsb.2005.5.1027
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