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On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients

Instituto de Matemática – UFRJ Av. Horácio Macedo, Centro de Tecnologia Cidade Universitária, Ilha do Fundão, 21941-972 Rio de Janeiro, RJ, Brazil

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Mahendra Panthee

IMECC, UNICAMP, 13083-859, Campinas, SP, Brazil

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, and

Marcia Scialom

IMECC, UNICAMP, 13083-859, Campinas, SP, Brazil

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https://doi.org/10.1142/S021919971450031XCited by:3 (Source: Crossref)

Abstract

We consider the Cauchy problem associated to the third-order nonlinear Schrödinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L²-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H¹ to the solution of the averaged equation.

Keywords:

AMSC: 35A01, 35Q53

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