THE INITIAL BOUNDARY VALUE PROBLEM FOR A CLASS OF NONLINEAR SCHRÖDINGER EQUATIONS

1986 ◽  
Vol 6 (4) ◽  
pp. 405-418 ◽  
Author(s):  
Yunmei Chen
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Initial Boundary Value

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 $\lambda$.

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