scholarly journals Nonhomogeneous Boundary Value Problems of Nonlinear Schrödinger Equations in a Half Plane

2018 ◽  
Vol 50 (3) ◽  
pp. 2773-2806 ◽  
Author(s):  
Yu Ran ◽  
Shu-Ming Sun ◽  
Bing-Yu Zhang
Keyword(s):  
Boundary Value Problems ◽  
Half Plane ◽  
Boundary Value ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonhomogeneous Boundary ◽  
Nonlinear Schrodinger Equations

scholarly journals Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space

2021 ◽  
Vol 2 (6) ◽  
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina ◽  
Takayoshi Ogawa
Keyword(s):  
Boundary Value Problem ◽  
Original Problem ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Dirichlet Boundary Value Problem ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

AbstractWe consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity in general space dimension $$n\ge 3$$ n ≥ 3 . We present some results on global existence in time and uniquness of small solutions to integral equations associated to the original problem.

Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrödinger Equations on the Half-line

2018 ◽  
Vol 19 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Bei-bei Hu ◽  
Tie-cheng Xia ◽  
Ning Zhang ◽  
Jin-bo Wang
Keyword(s):  
Boundary Value ◽  
Initial Boundary ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Half Line ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Initial Boundary Value

AbstractIn this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution $\{q_1(x,t),q_2(x,t)\}$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter $\lambda$.

Sign in / Sign up

Export Citation Format

Share Document