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http://dx.doi.org/10.4134/JKMS.j200257

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)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 835-847 More about this Journal
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
Schrodinger equation; numerical solution; eigenvalue problem;
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