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- W2946899652 abstract "We consider the Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation urn:x-wiley:mma:media:mma5698:mma5698-math-0001 on the line. The initial value q ( x ,0) is given and satisfies the symmetric, nonzero boundary conditions at infinity, that is, q ( x ,0)→ q ± as x →± ∞ , and | q ± |= q 0 >0. The goal of this paper is to study the asymptotic behavior of the solution of this initial value problem as t → ∞ . The main tool is the asymptotic analysis of an associated matrix Riemann‐Hilbert problem by using the steepest descent method and the so‐called g ‐function mechanism. We show that the solution q ( x , t ) of this initial value problem has a different asymptotic behavior in different regions of the x t ‐plane. In the regions and , the solution takes the form of a plane wave. In the region , the solution takes the form of a modulated elliptic wave." @default.
- W2946899652 created "2019-06-07" @default.
- W2946899652 creator A5029651470 @default.
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- W2946899652 date "2019-05-27" @default.
- W2946899652 modified "2023-10-16" @default.
- W2946899652 title "The Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation: Long‐time dynamics of nonzero boundary conditions" @default.
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- W2946899652 doi "https://doi.org/10.1002/mma.5698" @default.
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