J. Korean Math. Soc. 2021; 58(4): 835-847
Online first article November 26, 2020 Printed July 1, 2021
https://doi.org/10.4134/JKMS.j200257
Copyright © The Korean Mathematical Society.
Younghoon Kang, Eunjung Lee, Young-Ran Lee
Sogang University; Yonsei University; Sogang University
We study behavior of numerical solutions for a nonlinear eigenvalue problem on $\R^n$ that is reduced from a dispersion managed nonlinear Schr\"{o}dinger equation. The solution operator of the free Schr\"{o}dinger equation in the eigenvalue problem is implemented via the finite difference scheme, and the primary nonlinear eigenvalue problem is numerically solved via Picard iteration. Through numerical simulations, the results known only theoretically, for example the number of eigenpairs for one dimensional problem, are verified. Furthermore several new characteristics of the eigenpairs, including the existence of eigenpairs inherent in zero average dispersion two dimensional problem, are observed and analyzed.
Keywords: Schrodinger equation, numerical solution, eigenvalue problem
MSC numbers: 78M20, 65M06
Supported by: Young-Ran Lee and Eunjung Lee were supported by the National Research Foundation of Korea, NRF-2017R1D1A1B03033939 and NRF-2018R1D1A1B07042973, respectively.
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