Invariant tori for the Schrödinger equation in the Heisenberg Ferromagnetic chain. Issue 13 (3rd October 2019)

• Record Type: Journal Article
• Authors: Mi, Lufang; Cui, Wenyan
• Is Part Of: Applicable analysis. Volume 98:Issue 13(2019)
• Page Start: 2440
• Page End: 2453
• Publication Date: 2019-10-03
• Subjects: Heisenberg Ferromagnetic chain -- KAM theorem -- Schrödinger equation -- quasi-periodic solution -- normal form; 37K55 -- 35Q55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1460817
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: In this paper, we consider the nonlinear Heisenberg Ferromagnetic chain equation i u t + u xx - 2 u ¯ 1 + | u | 2 u x 2 = 0 under Dirichlet boundary conditions. By Taylor formula, the nonlinear Heisenberg Ferromagnetic chain equation can be described by the nonlinear Schrödinger type equation. Using an infinite dimensional KAM theorem for reversible system, we prove the existence of many n -dimensional invariant tori under sufficiently small perturbation and thus many time quasi-periodic solutions for the above equation.