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2013 QUASI-PERIODIC SOLUTIONS OF 1D NONLINEAR SCHRÖDINGER EQUATION WITH A MULTIPLICATIVE POTENTIAL
Xiufang Ren
Taiwanese J. Math. 17(6): 2191-2211 (2013). DOI: 10.11650/tjm.17.2013.3341

Abstract

This paper deals with one-dimensional (1D) nonlinear Schrödinger equation with a multiplicative potential, subject to Dirichlet boundary conditions. It is proved that for each prescribed integer $b\gt 1$, the equation admits small-amplitude quasi-periodic solutions, whose $b$-dimensional frequencies are small dilation of a given Diophantine vector. The proof is based on a modified infinite-dimensional KAM theory.

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Xiufang Ren. "QUASI-PERIODIC SOLUTIONS OF 1D NONLINEAR SCHRÖDINGER EQUATION WITH A MULTIPLICATIVE POTENTIAL." Taiwanese J. Math. 17 (6) 2191 - 2211, 2013. https://doi.org/10.11650/tjm.17.2013.3341

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1317.37095
MathSciNet: MR3141881
Digital Object Identifier: 10.11650/tjm.17.2013.3341

Subjects:
Primary: 37K55

Keywords: KAM theory , nonlinear Schrödinger equation , quasi-periodic solutions

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 6 • 2013
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