Quasi-periodic Solutions for Nonlinear Schrodinger Equations with Legendre Potential

In this paper, the nonlinear Schrödinger equations with Legendre potential iut − uxx + VL (x)u + mu + secx · |u|²u = 0 subject to certain boundary conditions is considered, where V L ( x ) = − 1 2 − 1 4 tan 2 x , x ∈ (−π/2, π/2). It is proved that for each given positive constant m > 0, the above...

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Published inTaiwanese journal of mathematics Vol. 24; no. 3; pp. 663 - 679
Main Authors Shi, Guanghua, Yan, Dongfeng
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2020
Online AccessGet full text
ISSN1027-5487
2224-6851
2224-6851
DOI10.11650/tjm/190707

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Abstract In this paper, the nonlinear Schrödinger equations with Legendre potential iut − uxx + VL (x)u + mu + secx · |u|²u = 0 subject to certain boundary conditions is considered, where V L ( x ) = − 1 2 − 1 4 tan 2 x , x ∈ (−π/2, π/2). It is proved that for each given positive constant m > 0, the above equation admits lots of quasi-periodic solutions with two frequencies. The proof is based on a partial Birkhoff normal form technique and an infinite-dimensional Kolmogorov-Arnold-Moser theory.
AbstractList In this paper, the nonlinear Schrödinger equations with Legendre potential iut − uxx + VL (x)u + mu + secx · |u|²u = 0 subject to certain boundary conditions is considered, where V L ( x ) = − 1 2 − 1 4 tan 2 x , x ∈ (−π/2, π/2). It is proved that for each given positive constant m > 0, the above equation admits lots of quasi-periodic solutions with two frequencies. The proof is based on a partial Birkhoff normal form technique and an infinite-dimensional Kolmogorov-Arnold-Moser theory.
Author Yan, Dongfeng
Shi, Guanghua
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Cites_doi 10.1007/978-3-662-08054-2
10.1002/cpa.20314
10.1007/s00208-013-1001-7
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10.1016/j.jde.2005.12.012
10.1155/S1073792894000516
10.1070/IM1989v032n01ABEH000733
10.3934/dcds.2006.16.615
10.1007/s00222-018-0812-2
10.24033/asens.2190
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10.1016/j.jfa.2004.10.019
10.1007/bf02104499
10.1016/j.jde.2011.10.006
10.4310/DPDE.2019.v16.n1.a2
10.3934/dcds.2017079
10.1088/0951-7715/24/4/010
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