American Institute of Mathematical Sciences

Advanced
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 & Continuous Dynamical Systems - B, 2005, 5 (4) : 1027-1042. doi: 10.3934/dcdsb.2005.5.1027
[1]

Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1565-1577. doi: 10.3934/dcdsb.2020173
[2]

Haoyu Li, Zhi-Qiang Wang. Multiple positive solutions for coupled Schrödinger equations with perturbations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020294
[3]

Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344
[4]

Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020379
[5]

Joel Kübler, Tobias Weth. Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3629-3656. doi: 10.3934/dcds.2020032
[6]

Chihiro Aida, Chao-Nien Chen, Kousuke Kuto, Hirokazu Ninomiya. Bifurcation from infinity with applications to reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3031-3055. doi: 10.3934/dcds.2020053
[7]

Susmita Sadhu. Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020342
[8]

Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084
[9]

Kuo-Chih Hung, Shin-Hwa Wang. Classification and evolution of bifurcation curves for a porous-medium combustion problem with large activation energy. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020281
[10]

Xianyong Chen, Weihua Jiang. Multiple spatiotemporal coexistence states and Turing-Hopf bifurcation in a Lotka-Volterra competition system with nonlocal delays. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021013

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences