Solitary waves on nonlocal Fermi–Pasta–Ulam lattices: Exponential localization. (December 2019)

• Record Type: Journal Article
• Authors: Pankov, Alexander
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 603
• Page End: 612
• Publication Date: 2019-12
• Subjects: Fermi–Pasta–Ulam lattice -- Nonlocal interaction -- Solitary wave -- Exponential localization; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.06.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The paper is devoted to Fermi–Pasta–Ulam lattices with nonlocal interaction. Under natural assumptions we show that all solitary traveling waves are exponentially localized. We reduce the problem to a linear eigenvalue problem for certain integral operator. Then we use functional analysis tools and exponentially weighted spaces of functions to prove the localization of solitary waves.