The Unified Transform Method to Initial-Boundary Value Problem for a Coupled Cubic–Quintic Nonlinear Schrödinger System

2018 ◽  
Vol 13 (3) ◽  
pp. 1143-1159 ◽  
Author(s):  
Beibei Hu ◽  
Tiecheng Xia ◽  
Ning Zhang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Transform Method ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Unified Transform Method ◽  
Initial Boundary Value ◽  
Schrödinger System

scholarly journals On an initial-boundary value problem for the nonlinear Schrödinger equation

1979 ◽  
Vol 2 (3) ◽  
pp. 503-522 ◽  
Author(s):  
Herbert Gajewski
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Initial Boundary Value

We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.

scholarly journals The initial-boundary value problem for the Schrödinger–Korteweg–de Vries system on the half-line

2019 ◽  
Vol 21 (08) ◽  
pp. 1850066 ◽  
Author(s):  
Márcio Cavalcante ◽  
Adán J. Corcho
Keyword(s):  
Boundary Value Problem ◽  
Vries Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Half Line ◽  
Nonlinear Schrödinger ◽  
De Vries ◽  
Quadratic Nonlinearities ◽  
Initial Boundary Value

We prove local well-posedness for the initial-boundary value problem (IBVP) associated to the Schrödinger–Korteweg–de Vries system on right and left half-lines. The results are obtained in the low regularity setting by using two analytic families of boundary forcing operators, one of these families being developed by Holmer to study the IBVP associated to the Korteweg–de Vries equation [The initial-boundary value problem for the Korteweg–de Vries equation, Comm. Partial Differential Equations 31 (2006) 1151–1190] and the other one was recently introduced by Cavalcante [The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line, Differential Integral Equations 30(7–8) (2017) 521–554] in the context of nonlinear Schrödinger with quadratic nonlinearities.

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