Self-similar solutions for the 1-D Schrödinger map on the hyperbolic plane

Author： Hoz Francisco  

Publisher： Springer Publishing Company

ISSN： 0025-5874

Source： Mathematische Zeitschrift, Vol.257, Iss.1, 2007-09, pp. : 61-80

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Abstract

In this paper, we will study self-similar solutions for X t = XX ss , the equivalent in the Minkowski 3-space to the localized induction approximation flow, trying to adapt some results given by Gutiérrez, Rivas and Vega. We will show the existence of a one-parameter family of smooth solutions developing a corner in finite time. The main difference with respect to the Euclidean case studied by those authors will be the proof of the boundedness of T, e 1 and e 2, the equivalents of T, b and n in .

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