Spatial heteroclinic bifurcation of time periodic solutions to the Ginzburg-Landau equation

Dang-Vu, H.; Delcarte, C.

doi:10.1090/qam/1770649

Authors: H. Dang-Vu and C. Delcarte
Journal: Quart. Appl. Math. 58 (2000), 459-472
MSC: Primary 35Q55; Secondary 34C37, 35B10, 37D45, 37L10
DOI: https://doi.org/10.1090/qam/1770649
MathSciNet review: MR1770649
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Abstract: In this paper we study the spatial structure of the time periodic solutions to the Ginzburg-Landau equation in various configurations (supercritical and subcritical). We show that spatially periodic bursting solutions or spatially heteroclinic solutions can occur depending upon the values of the coefficients. As a consequence of this study, we obtain an exact solution to the nonlinear system of Kapitula and Maier-Paape [16]. We then show that near a spatially heteroclinic solution there is an extremely intricate complex of spatially unstable solutions and KAM surfaces.

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