The initial-boundary value problem for Schr\"odinger-Korteweg-de Vries system on the half-line
Analysis of PDEs
2018-10-05 v4
Abstract
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-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 Schr\"odinger with quadratic nonlinearities.
Keywords
Cite
@article{arxiv.1608.06308,
title = {The initial-boundary value problem for Schr\"odinger-Korteweg-de Vries system on the half-line},
author = {Adán J. Corcho and Márcio Cavalcante},
journal= {arXiv preprint arXiv:1608.06308},
year = {2018}
}
Comments
38 pages, 2 figures, final version, to appear in Communications in Contemporary Mathematics