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The WKB method and geometric instability for non linear Schrodinger equations on surfaces

Laurent Thomann
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Abstract

In this paper we are interested in constructing WKB approximations for the non linear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.

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Laurent Thomann. 2006-09-29. The WKB method and geometric instability for non linear Schrodinger equations on surfaces. https://arxiv.org/abs/math/0609805

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