Quasi-periodic solutions of NLS with Liouvillean Frequency
Xindong Xu, Jiangong You, Qi Zhou
TL;DR
This paper constructs quasi-periodic solutions with Liouvillean frequency for the forced nonlinear Schrödinger equation using an advanced infinite dimensional KAM theory, expanding the understanding of such solutions in complex dynamical systems.
Contribution
It introduces a novel application of infinite dimensional KAM theory to establish quasi-periodic solutions with Liouvillean frequency for NLS equations, which was previously unaddressed.
Findings
Existence of quasi-periodic solutions with Liouvillean frequency for NLS
Application of infinite dimensional KAM theory to Liouvillean frequencies
Extension of solution techniques to more general frequency conditions
Abstract
Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schr\"odinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean frequency.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Photonic Systems · Laser-Matter Interactions and Applications