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

2016/08/22 by Corcho, Adán J., Cavalcante, Márcio
#35B65 #35Q53 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.06308

Abstract

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, being one of these family developed by Holmer to study the IBVP associated to the Korteweg-de Vries equation (Communications in Partial Differential Equations, 31 (2006)) and the other family one was recently introduced by Cavalcante (Differential and Integral Equations (2017)) in the context of nonlinear Schrödinger with quadratic nonlinearities.

Related

• The initial-boundary value problem for the Korteweg-de Vries equation
• The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line
• Well-posedness for the Schrodinger-KdV system on the half-line
• Well-Posedness of the Nonlinear Schrödinger Equation on the Half-Plane
• Well-posedness and long time behavior for the Schrödinger-Korteweg-de Vries interactions on the half-Line