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Numerical solution of the nonlinear Schrödinger equation in the radiallysymmetric case

A.A. Degtyarev, A.E. Derkach

Samara State Aerospace University

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Pages: 14-18.

Full text of article: Russian language.

Abstract:
To solve the Schrödinger equation describing the propagation of an electromagnetic wave in a nonlinear medium, the authors use a conservative difference scheme with the iterative improvement, which has the quadratic order of accuracy in the direction of wave propagation, and the order of accuracy close to quadratic in the radial variable. The results obtained in computational experiments fully confirm the theoretical studies. An important feature of this method is that it allows to simulate the process of wave propagation in a nonlinear medium over a distance of tens of meters.

Citation:
Degtyarev AA, Derkach AE. Numerical solution of the nonlinear Schrödinger equation in the radially-symmetric case. Computer Optics 2001; 21: 14 - 18.

References:
  1. Vinogradova MB, Rudenko OV, Sukhorukov AP. Theory of waves [In Russian]. Moscow: "Nauka" Publisher; 1979.
  2. Karamzin YN, Sukhorukov AP, Trofimov VA. Mathematical modeling in nonlinear optics [In Russian]. Moscow: MGU Publisher; 1989.
  3. Samarskii AA. The theory of difference schemes. CRC Press; 2001.
  4. Adams MJ. An introduction to optical waveguides. New York: John Wiley & Sons Inc; 1981.

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