Dissipative property for higher order nonlinear Schrödinger equation. (November 2019)

• Record Type: Journal Article
• Authors: Naumkin, Pavel I.; Sánchez-Suárez, Isahi
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 91
• Page End: 124
• Publication Date: 2019-11
• Subjects: 35B40 -- 35Q92 -- 92B05; Nonlinear Schrödinger equation -- Dispersive equations -- Scattering theory -- Decay estimates; 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.2019.05.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation (0.1) i ∂ t u + 1 2 ∂ x 2 u − 1 4 ∂ x 4 u = i 3 λ 1 u 3 + λ 2 u 2 u, t > 1, x ∈ R, u 1, x = u 0 x, x ∈ R, where the coefficients 0 < λ 1 < λ 2 . The aim of the present paper is to prove the global existence of solutions to (??). Also we find the large time decay estimates for the solutions.