Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line

Date
2021-09
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Source Title
Mathematical Inequalities & Applications
Print ISSN
1331-4343
Electronic ISSN
1848-9966
Publisher
Element d.o.o.
Volume
25
Issue
2
Pages
551 - 571
Language
English
Type
Article
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Abstract

In this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr¨odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally require highly technical approaches, as opposed to our simple treatment which is based on constructing a boundary integral operator of oscillatory nature via the Fokas method. Our method is uniform and can be extended to other higher order partial differential equations where the main equation possibly involves more than one spatial derivatives.

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Keywords
Fourth order Schrödinger equation, Unified transform method, Fokas method, Wellposedness
Citation
Published Version (Please cite this version)