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On separability of non-linear Schrodinger operators with matrix potentials

  • Hany A. Atia EMAIL logo , H. M. Abu-Donia and F. Mahmoud Ellaithy
Published/Copyright: May 4, 2021

Abstract

In this paper, we studied the separability of the non-linear Schrodinger operator of the form S u x = Δ u x + V x , u u x ,  where  Δ u x = i = 1 n 2 u x x i 2 , with the non-linear matrix potential V x , u . We obtained the sufficient conditions for separability of this operator in the space L 2 R n and we established the suitable coercive inequalities.

AMS subject classification: 47F05; 58J99

Corresponding author: Hany A. Atia, Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2020-02-21
Accepted: 2021-03-29
Published Online: 2021-05-04
Published in Print: 2022-10-27

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