The Riemann–Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line
نویسندگان
چکیده
We derive the long-time asymptotics for solution of initial-boundary value problem coupled nonlinear Schrodinger equation whose Lax pair involves 3 × matrix in present paper. Based on a no...
منابع مشابه
Estimate for the Schrödinger Equation on the Half - Line ∗
In this paper we prove the L p − L ´ p estimate for the Schrödinger equation on the half-line and with homogeneous Dirichlet boundary condition at the origin.
متن کاملThe coupled modified nonlinear Schrödinger equations on the half - line via the Fokas method ∗
Coupled modified nonlinear Schrödinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initialboundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x, t) and v(x, t) of CMNLS equations are exists, and we show that it can be expre...
متن کاملThe derivative nonlinear Schrödinger equation on the half-line
We analyze the derivative nonlinear Schrödinger equation iqt + qxx = i ( |q|q ) x on the half-line using the Fokas method. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x, t dependence and is given in terms of the ...
متن کاملThe Derivative Nonlinear Schrödinger Equation on the Half Line
We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost sharp local wellposedness, nonlinear smoothing, and small data global wellposedness in the energy space. One of the obstructions is that the crucial gauge transf...
متن کاملThe Initial-boundary Value Problem for the 1d Nonlinear Schrödinger Equation on the Half-line
We prove, by adapting the method of Colliander-Kenig [9], local wellposedness of the initial-boundary value problem for the one-dimensional nonlinear Schrödinger equation i∂tu+∂ 2 x u+λu|u|α−1 = 0 on the half-line under low boundary regularity assumptions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: ['1776-0852', '1402-9251']
DOI: https://doi.org/10.1080/14029251.2019.1613055