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Analytical and Numerical Investigation of Soliton Solutions of Coupled Equations in Quadratic Media: A Novel Approach

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Author(s): Alireza Heidari | Seyedali Vedad

Journal: Studies in Mathematical Sciences
ISSN 1923-8444

Volume: 4;
Issue: 2;
Start page: 54;
Date: 2012;
Original page

Keywords: Bright and dark solitons | Spatial optical soliton | Quadratic Kerr media | Variational method | Secondharmonic generation

ABSTRACT
Solitons have been hitherto studied in Kerr media. However, we show that the optical solitons are not only limited to non-linear Kerr media. In this paper, a new method is devised to achieve the analytical approximate solutions to the soliton packages in one and two dimensions. Inputting (1) and (2) to Maxwell equations and using second-harmonic generation of type I, the coupled motion equations are obtained. Some states of spatial bright solitons are studied for large values of . The variational method is briefly reviewed and analytical approximate solution to quadratic-soliton coupled motion equations is investigated in one and two dimensions and also numerically solved. The comparison of analytical and numerical results indicates that our method is more accurate than the variational method.Key words Bright and dark solitons; Spatial optical soliton; Quadratic Kerr media; Variational method; Secondharmonic generation
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