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Type: Artigo
Title: On the periodic Cauchy problem for a coupled system of third-order nonlinear Schrödinger equations
Author: Scialom, M.
Bragança, L. M.
Abstract: We investigate some well-posedness issues for the initial value problem (IVP) associated to the system {2i∂tu+q∂x2u+iΓ∂x3u=F1(u,w)2i∂tw+q∂x2w+iΓ∂x3w=F2(u,w),where F1 and F2 are polynomials of degree 3 involving u, w and their derivatives. This system describes the dynamics of two nonlinear short-optical pulses envelopes u(x, t) and w(x, t) in fibers (Hasegawa and Kodama in IEEE J Quantum Electron 23(5):510–524, 1987; Porsezian et al. in Phys Rev E 50:1543–1547, 1994). We prove periodic local well-posedness for the IVP with data in Sobolev spaces Hs(T) × Hs(T) , s≥ 1 / 2 and global well-posedness result in Sobolev spaces H1(T) × H1(T)
Subject: Equação não-linear de Schrodinger
Problema de Cauchy
Country: Alemanha
Editor: Springer
Rights: Fechado
Identifier DOI: 10.1007/s40863-019-00143-6
Date Issue: 2019
Appears in Collections:IMECC - Artigos e Outros Documentos

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