Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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NUMERICAL SOLUTIONS FOR ONE AND TWO DIMENSIONAL NONLINEAR PROBLEMS RELATED TO DISPERSION MANAGED SOLITONS

  • Kang, Younghoon (Department of Mathematics Sogang University) ;
  • Lee, Eunjung (Department of Computational Science and Engineering Yonsei University) ;
  • Lee, Young-Ran (Department of Mathematics Sogang University)
  • Received : 2020.05.09
  • Accepted : 2020.09.21
  • Published : 2021.07.01
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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.

Keywords

Acknowledgement

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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