A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimension

Article type: Research Article

Authors: Kim, Donghyun

Affiliations: Research and Industry-University Cooperation Foundation, Hankuk University of Foreign Studies, Imun-ro 107, Dongdaemun-gu, Seoul 130-791, Korea. E-mail: [email protected]

Abstract: We consider the initial value problem for a system of cubic nonlinear Schrödinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution exists globally and decays at the rate O(t−1/2(logt)−1/2) in L∞ as t tends to infinity, if the system satisfies certain mass relations.

Keywords: NLS system, nonlinear dissipation, time-decay, critical nonlinearity

DOI: 10.3233/ASY-161362

Journal: Asymptotic Analysis, vol. 98, no. 1-2, pp. 79-90, 2016