Abstract. The paper deals with finding of soliton solution for Schrödinger equation with periodic linear and nonlinear properties of medium in 1D case. Such structure is named as photonic crystal. To find soliton solution the corresponding problem for finding of eigenfunctions and eigenvalues is formulated. Iterative process is proposed for solution of this problem. Using the technique of continuation on parameter we investigate a dependence of soliton location on its maximum intensity, on ratio between light frequency and frequency of structure, on ratio between dielectric permittivity of alternating linear and nonlinear layers and on position between centre of initial distribution of eigenfunction and center of considered photonic structure area. The results of this paper confirm the features of soliton self-formation investigated early in our papers [37,38,39,40,41,42], in which one considered a propagation of femtosecond laser pulse through nonlinear layered structure.
Abstract. The paper describes the iteration method for finding the eigenfunctions and eigenvalues of the system of two nonlinear Schrödinger equations, which describes the process of second harmonic generation by femtosecond pulse in media with the quadratic and cubic nonlinear response. Coefficients, which characterize the nonlinearities, depend on one of the coordinate. The discussed method allows to find soliton solutions of new form corresponding to the first and second eigenvalues for the wide range of the nonlinear coefficients values. For determination of the eigenfunctions of the third and higher order it is necessary to select the initial approximation in a special way.
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