Target phase waves for over-damped sine Gordon equation. These waves appear in the presence of thermal fluctuations as a result of competition between arrested and cycling states, close to the transition point.
The over-damped sine Gordon equation can be derived as a special case of the complex Ginzburg-Landau equation supplemented with a continuous-symmetry breaking term [1].
Reference : I. S. Aranson and L. Kramer, The World of the Complex Ginzburg-Landau equation, Rev. Mod. Phys. 74, 99 (2002).
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