Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition

Abstract

© 2017 American Mathematical Society. The Gerdjikov-Ivanov (GI) type of derivative nonlinear Schrödinger equation is considered on the quarter plane whose initial data vanish at infinity while boundary data are time-periodic, of the form ae iδ e 2iωt . The main purpose of this paper is to provide the long-time asymptotics of the solution to the initial-boundary value problems for the equation. For ω < b 0, t > 0~, on which the asymptotics admit qualitatively different forms. In the region x > 4tb, the solution is asymptotic to a slowly decaying self-similar wave of Zakharov- Manakov type. In the region 0 < x, < 4t(b-√2a 2 (a 2 /4-b)), the solution takes the form of a plane wave. In the region 4t(b-√2a 2 (a 2 /4-b)) < x < 4tb, the solution takes the form of a modulated elliptic wave.