## Taiwanese Journal of Mathematics

### QUASI-PERIODIC SOLUTIONS OF 1D NONLINEAR SCHRÖDINGER EQUATION WITH A MULTIPLICATIVE POTENTIAL

Xiufang Ren

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 6 (2013), 2191-2211.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706292

Digital Object Identifier
doi:10.11650/tjm.17.2013.3341

Mathematical Reviews number (MathSciNet)
MR3141881

Zentralblatt MATH identifier
1317.37095

Subjects
Primary: 37K55: Perturbations, KAM for infinite-dimensional systems

#### Citation

Ren, Xiufang. QUASI-PERIODIC SOLUTIONS OF 1D NONLINEAR SCHRÖDINGER EQUATION WITH A MULTIPLICATIVE POTENTIAL. Taiwanese J. Math. 17 (2013), no. 6, 2191--2211. doi:10.11650/tjm.17.2013.3341. https://projecteuclid.org/euclid.twjm/1499706292

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