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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Bibliographic Details
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
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ISSN1027-5487
2224-6851
DOI10.11650/tjm/190707

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Summary: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.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/190707