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Stability of standing waves for nonlinear defocusing fourth‐order dispersive Schrödinger equation with unbounded potentials
Author(s) -
Chen Guanggan,
Zhang Jian,
Wei Yunyun
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510621
Subject(s) - nonlinear system , mathematics , stability (learning theory) , standing wave , order (exchange) , nonlinear schrödinger equation , dispersive partial differential equation , mathematical analysis , schrödinger's cat , schrödinger equation , physics , acoustics , partial differential equation , quantum mechanics , computer science , finance , machine learning , economics
Abstract This paper is concerned with a nonlinear defocusing fourth‐order dispersive Schrödinger equation with unbounded potentials which models propagation in fiber arrays. We analyze the global existence of the solution and also obtain the existence of the standing waves for the system. Furthermore, we prove that the standing waves are orbitally stable. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)