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2004 Schrödinger group on Zhidkov spaces
Clément Gallo
Adv. Differential Equations 9(5-6): 509-538 (2004).

Abstract

We consider the Cauchy problem for nonlinear Schrödinger equations on $\mathbb{R}^{n}$ with nonzero boundary condition at infinity, a situation which occurs in stability studies of dark solitons. We prove that the Schrödinger operator generates a group on Zhidkov spaces $X^{k}(\mathbb{R}^{n})$ for $k>n/2$, and that the Cauchy problem for NLS is locally well-posed on the same Zhidkov spaces. We justify the conservation of classical invariants which implies in some cases the global well-posedness of the Cauchy problem.

Citation

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Clément Gallo. "Schrödinger group on Zhidkov spaces." Adv. Differential Equations 9 (5-6) 509 - 538, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 0476.03047
MathSciNet: MR2099970

Subjects:
Primary: 35Q55
Secondary: 35A30, 47H20

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 5-6 • 2004
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