This article is cited in 13 papers

Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity

O. V. Matusevich, V. A. Trofimov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: An iterative method is proposed to determine the eigenfunctions of a system of two nonlinear Schrödinger equations governing the interaction of two femtosecond pulses in a medium with quadratic and cubic nonlinearity. The method produces soliton solutions of a new form for a wide range of nonlinearity coefficients corresponding to the first and second eigenvalues. A specially chosen initial approximation is required to determine the third and higher eigenfunctions.

Key words: nonlinear Schrödinger equation, iterative method, eigenfunction, eigenvalue, soliton, femtosecond pulse.

UDC: 519.634

Received: 14.05.2007
Revised: 22.10.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:4, 677–687

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