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The nonhomogeneous boundary-value problems for the 1D-NLS equation with lineal boundary condition

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Abstract

In this paper, we study the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with different inhomogeneous boundaries data. We study the well-posedness in the case of Neumann and Robin condition in Sobolev space of low regularity. Also, we revisit, in a self-consistent way, some results concerning the Dirichlet condition.

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Acknowledgements

L. Esquivel would like to express his gratitude to University of Valle, Department of Mathematics for all the facilities used along the realization of this work.

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  1. Liliana Esquivel and Juan Carlos López have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del Valle, Cali, Colombia

    Liliana Esquivel

  2. Departamento de Matemáticas, Universidad de Pamplona, Pamplona, Colombia

    Juan Carlos López

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  1. Liliana Esquivel
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  2. Juan Carlos López
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Both authors have contributed equally to the paper.

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Correspondence to Liliana Esquivel.

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Communicated by Jaime Angulo Pava.

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Esquivel, L., López, J.C. The nonhomogeneous boundary-value problems for the 1D-NLS equation with lineal boundary condition. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00439-2

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