NUMERICAL SOLUTIONS FOR ONE AND TWO DIMENSIONAL NONLINEAR PROBLEMS RELATED TO DISPERSION MANAGED SOLITONS

초록

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 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.

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