On the spatial asymptotics of solutions of the Ablowitz-Ladik hierarchy

Author:
Johanna Michor

Journal:
Proc. Amer. Math. Soc. **138** (2010), 4249-4258

MSC (2010):
Primary 37K40, 37K15; Secondary 35Q55, 37K10

DOI:
https://doi.org/10.1090/S0002-9939-2010-10595-6

Published electronically:
July 20, 2010

MathSciNet review:
2680051

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Abstract: We show that for decaying solutions of the Ablowitz-Ladik system, the leading asymptotic term is time independent. In addition, two arbitrary bounded solutions of the Ablowitz-Ladik system which are asymptotically close at the initial time stay close. All results are also derived for the associated hierarchy.

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Additional Information

**Johanna Michor**

Affiliation:
Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria – and – International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria

Email:
Johanna.Michor@univie.ac.at

DOI:
https://doi.org/10.1090/S0002-9939-2010-10595-6

Keywords:
Spatial asymptotics,
Ablowitz–Ladik hierarchy

Received by editor(s):
September 16, 2009

Published electronically:
July 20, 2010

Additional Notes:
This research was supported by the Austrian Science Fund (FWF) under Grant No. V120

Dedicated:
Dedicated with great pleasure to Peter W. Michor on the occasion of his 60th birthday

Communicated by:
Peter A. Clarkson

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.