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Solutions of mKdV in classes of functions unbounded at infinity


Kappeler, T; Perry, P; Shubin, M; Topalov, P (2008). Solutions of mKdV in classes of functions unbounded at infinity. Journal of Geometric Analysis, 18(2):443-477.

Abstract

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.

Abstract

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:April 2008
Deposited On:14 Jan 2009 15:52
Last Modified:06 Dec 2017 15:45
Publisher:Springer
ISSN:1050-6926
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s12220-008-9013-3
Related URLs:http://arxiv.org/abs/math/0601237
http://www.ams.org/mathscinet-getitem?mr=2393267

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