On small energy stabilization in the NLKG with a trapping potential. (November 2016)

• Record Type: Journal Article
• Authors: Cuccagna, Scipio; Maeda, Masaya; Phan, Tuoc V.
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 32
• Page End: 58
• Publication Date: 2016-11
• Subjects: Nonlinear Klein Gordon equation -- Asymptotic stability -- Birkhoff normal forms -- Hamiltonian system; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.08.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a nonlinear Klein Gordon equation (NLKG) with short range potential with eigenvalues and show that in the contest of complex valued solutions the small standing waves are attractors for small solutions of the NLKG. This extends the results already known for the nonlinear Schrödinger equation and for the nonlinear Dirac equation. In addition, this extends a result of Bambusi and Cuccagna (which in turn was an extension of a result by Soffer and Weinstein) which considered only real valued solutions of the NLKG.