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A new way for decreasing of amplitude of wave reflected from artificial boundary condition for 1D nonlinear Schrödinger equation

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  • In this report, we focus on computation performance enhancing at computer simulation of a laser pulse interaction with optical periodic structure (photonic crystal). Decreasing the domain before the photonic crystal one can essentially increases a computation performance. With this aim, firstly, we provide a computation in linear medium and storage the complex amplitude at chosen section of coordinate along which a laser light propagates. Then we use this time-dependent value of complex amplitude as left boundary condition for the 1D nonlinear Schrödinger equation in decreased domain containing a nonlinear photonic crystal. Because a part of a laser pulse reflects from faces of photonic crystal layers, we use artificial boundary condition. To decrease amplitude of the wave reflected from artificial boundary we introduce in consideration some additional number of waves related with the equation under consideration.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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    E.B. Tereshin, V.A. Trofimov and M.V.Fedotov, Conservative finite difference scheme for the problem of propagation of a femtosecond pulse in a nonlinear photonic crystal with non-reflecting boundary conditions, Comp Math and Math Physics, 46:1 (2006), 154-164.


    V.A. Trofimov and P.V. Dogadushkin, Boundary conditions for the problem of femtosecond pulse propagation in absorption layered structure, Proceedings of Fourth Int Conf Finite Diff Methods: Theory and app, Rouse University Angel Kanchev, Lozenetz, Bulgaria, (2007), 307-313.


    Z. Xuand and H. Han, Absorbing boundary conditions for nonlinear Schrödinger equations, Phys Rev, 74:037704 (2006).


    C. Zheng, Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations, J Comput Phys, 215 (2006), 552-565.

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