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

Instituto de Matemática, Universidade Federal de Alagoas, Campus A.C. Simões, Av. Lourival Melo Mota, s/n, Tabuleiro do Martins 57072-900, Maceió, Alagoas, Brazil

E-mail Address: marcio.melo@im.ufal.br

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and

Adán J. Corcho

Instituto de Matemática, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Bloco C. Cidade Universitária, Ilha do Fundão 21941-909, Rio de Janeiro, RJ, Brazil

E-mail Address: adan@im.ufrj.br

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https://doi.org/10.1142/S0219199718500669Cited by:10 (Source: Crossref)

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, one of these families being developed by Holmer to study the IBVP associated to the Korteweg–de Vries equation [The initial-boundary value problem for the Korteweg–de Vries equation, Comm. Partial Differential Equations31 (2006) 1151–1190] and the other one was recently introduced by Cavalcante [The initial-boundary value problem for some quadratic nonlinear Schrödinger equations on the half-line, Differential Integral Equations30(7–8) (2017) 521–554] in the context of nonlinear Schrödinger with quadratic nonlinearities.

Keywords:

AMSC: 35Q53, 35Q55, 35B65

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