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Asymptotic analysis of a new type of multi-bump, self-similar, blowup solutions of the Ginzburg–Landau equation

Published online by Cambridge University Press:  29 October 2012

V. ROTTSCHÄFER
V. ROTTSCHÄFER*
Affiliation:
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, the Netherlands email: vivi@math.leidenuniv.nl
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Abstract

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We study of a new type of multi-bump blowup solutions of the Ginzburg–Landau equation. Multi-bump blowup solutions have previously been found in numeric simulations, asymptotic analysis and were proved to exist via geometric construction. In the geometric construction of the solutions, the existence of two types of multi-bump solutions was shown. One type is exponentially small at ξ=0, and the other type of solutions is algebraically small at ξ=0. So far, the first type of solutions were studied asymptotically. Here, we analyse the solutions which are algebraically small at ξ=0 by using asymptotic methods. This construction is essentially different from the existing one, and ideas are obtained from the geometric construction. Hence, this is a good example of where both asymptotic analysis and geometric methods are needed for the overall picture.

Keywords

Ginzburg–Landau equationMulti-bump blowup solutions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 1 , February 2013 , pp. 103 - 129
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
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Copyright
Copyright © Cambridge University Press 2012

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