Universität zu Köln

Pelinovsky, Dmitry E., Saalmann, Aaron and Shimabukuro, Yusuke (2017). The derivative NLS equation: global existence with solitons. Dyn. Partial Differ. Equ., 14 (3). S. 271 - 295. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1548-159X

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Abstract

We prove the global existence result for the derivative NLS equation in the case when the initial datum includes a finite number of solitons. This is achieved by an application of the Backlund transformation that removes a finite number of zeros of the scattering coefficient. By means of this transformation, the Riemann-Hilbert problem for meromorphic functions can be formulated as the one for analytic functions, the solvability of which was obtained recently. A major difficulty in the proof is to show invertibility of the Backlund transformation acting on weighted Sobolev spaces.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Pelinovsky, Dmitry E. UNSPECIFIED UNSPECIFIED UNSPECIFIED Saalmann, Aaron UNSPECIFIED UNSPECIFIED UNSPECIFIED Shimabukuro, Yusuke UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-245296
Journal or Publication Title:	Dyn. Partial Differ. Equ.
Volume:	14
Number:	3
Page Range:	S. 271 - 295
Date:	2017
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1548-159X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NONLINEAR SCHRODINGER-EQUATION; INVERSE SCATTERING; SOLITARY WAVES; WELL-POSEDNESS; STABILITY Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24529