scholarly journals Multi-bump, self-similar, blow-up solutions of the Ginzburg–Landau equation

2008 ◽  
Vol 237 (4) ◽  
pp. 510-539 ◽  
Author(s):  
Vivi Rottschäfer
Keyword(s):  
Blow Up ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Self Similar

Exact periodic and blow up solutions for 2D Ginzburg–Landau equation

2008 ◽  
Vol 373 (1) ◽  
pp. 19-22 ◽  
Author(s):  
Penghong Zhong ◽  
Ronghui Yang ◽  
Ganshan Yang
Keyword(s):  
Blow Up ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

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

2012 ◽  
Vol 24 (1) ◽  
pp. 103-129 ◽  
Author(s):  
V. ROTTSCHÄFER
Keyword(s):  
Asymptotic Analysis ◽  
Landau Equation ◽  
Asymptotic Methods ◽  
Geometric Construction ◽  
The Other ◽  
Ginzburg Landau ◽  
Geometric Methods ◽  
Ginzburg Landau Equation ◽  
New Type ◽  
Self Similar

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.

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