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June, 2020 Quasi-periodic Solutions for Nonlinear Schrödinger Equations with Legendre Potential
Guanghua Shi, Dongfeng Yan
Taiwanese J. Math. 24(3): 663-679 (June, 2020). DOI: 10.11650/tjm/190707


In this paper, the nonlinear Schrödinger equations with Legendre potential $\mathbf{i} u_{t} - u_{xx} + V_L(x)u + mu + \sec x \cdot |u|^2 u = 0$ subject to certain boundary conditions is considered, where $V_L(x) = -\frac{1}{2} - \frac{1}{4} \tan^2 x$, $x \in (-\pi/2,\pi/2)$. It is proved that for each given positive constant $m \gt 0$, 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.


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Guanghua Shi. Dongfeng Yan. "Quasi-periodic Solutions for Nonlinear Schrödinger Equations with Legendre Potential." Taiwanese J. Math. 24 (3) 663 - 679, June, 2020.


Received: 10 August 2018; Revised: 3 May 2019; Accepted: 28 July 2019; Published: June, 2020
First available in Project Euclid: 19 May 2020

zbMATH: 07251191
MathSciNet: MR4100713
Digital Object Identifier: 10.11650/tjm/190707

Primary: 37C55 , 37K55

Keywords: Kolmogorov-Arnold-Moser theory , quasi-periodic solutions , singular differential operator

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 3 • June, 2020
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