Dissipative property for higher order nonlinear Schrödinger equation. (November 2019) - Naumkin, Pavel I.; Sánchez-Suárez, Isahi
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.