Abstract
In this short note we present results on the existence of several classes of travelling, non- periodic solutions of the complex Ginzburg-Landau equation. First we give a very short introduction to the G-L equation and show its importance in nonlinear stability theory. We then study the G-L equation with complex coefficients and establish the existence of a 2-parameter family of quasi-periodic solutions and two different types of one-parameter families of heteroclinic orbits; all members of these families travel with a well-defined wave-speed. The heteroclinic solutions correspond to (travelling) soliton-like ‘localized structures’ which connect different (stable) periodic patterns. Mathematically, these families of travelling solutions (quasi-periodic and heteroclinic) are continuations into the complex case of the stationary solutions of the real G-L equation.
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© 1993 Springer Science+Business Media Dordrecht
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Doelman, A. (1993). Travelling, Non-Periodic Patterns in Nonlinear Stability Problems. In: Nieuwstadt, F.T.M. (eds) Advances in Turbulence IV. Fluid Mechanics and its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1689-3_7
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DOI: https://doi.org/10.1007/978-94-011-1689-3_7
Publisher Name: Springer, Dordrecht
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