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

作者：Rottschafer V^*

来源：European Journal of Applied Mathematics, 2013, 24(1): 103-129.

DOI：10.1017/S0956792512000320

• Ginzburg-Landau equation
• Multi-bump blowup solutions

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 xi = 0, and the other type of solutions is algebraically small at xi = 0. So far, the first type of solutions were studied asymptotically. Here, we analyse the solutions which are algebraically small at xi = 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.

• 出版日期2013-2