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

Adán J. Corcho, Márcio C. Melo

Published 2016-08-22Version 1

We prove local well-posedness for the initial-boundary value problem (IBVP) associated to the Schr\"odinger-Korteweg de Vries system on right and left half-line. The results are obtained in the low regularity setting by the using two analytic families of boundary forcing operators, one of these family was developed by Holmer for the IBVP associated to the Korteweg-de Vries equation (Communications in Partial Differential Equations, 31 (2006)) and the other one was recently introduced by Melo in the context of nonlinear Schr\"odinger with quadratic nonlinearities.