The initial-boundary value problem for some quadratic nonlinear\n Schr "odinger equations on the half-line

2016/01/11 by Márcio Cavalcante, Cavalcante, Márcio, Márcio André Araújo Cavalcante
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1601.02565

openalex publication_date 2016/01/11 · openalex created_date 2023/01/03 · openalex updated_date 2026/07/28

Abstract

We prove local well-posedness for the initial-boundary-value problem\nassociated to some quadratic nonlinear Schr "odinger equations on the\nhalf-line. The results are obtained in the low regularity setting by\nintroducing an analytic family of boundary forcing operators, following the\nideas developed by Colliander, Kenig and Holmer.\n

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