Abstract
We study behavior of numerical solutions for a nonlinear eigenvalue problem on Rn that is reduced from a dispersion managed nonlinear Schrödinger equation. The solution operator of the free Schrödinger 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.
| Original language | English |
|---|---|
| Pages (from-to) | 835-847 |
| Number of pages | 13 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 58 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2021 |
Bibliographical note
Funding Information:Received May 9, 2020; Revised September 12, 2020; Accepted September 21, 2020. 2010 Mathematics Subject Classification. 78M20, 65M06. Key words and phrases. Schrodinger equation, numerical solution, eigenvalue problem. Young-Ran Lee and Eunjung Lee were supported by the National Research Foundation of Korea, NRF-2017R1D1A1B03033939 and NRF-2018R1D1A1B07042973, respectively.
Publisher Copyright:
© 2021 Korean Mathematical Society.
All Science Journal Classification (ASJC) codes
- Mathematics(all)