Numerical solutions for one and two dimensional nonlinear problems related to dispersion managed solitons
J. Korean Math. Soc. Published online November 26, 2020
Younghoon Kang, Eunjung Lee, and Young-Ran Lee
Sogang University, Yonsei University
Abstract : We study behavior of numerical solutions for a nonlinear eigenvalue problem on R^n that is reduced from a dispersion managed nonlinear Schrodinger equation. The solution operator of the free Schrodinger 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 one and two dimensional numerical simulations, novel characteristics of the eigenpairs obtained from the numerical solutions are observed and analyzed.
Keywords : Schrodinger equation, Numerical solution, Eigenvalue problem