Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity
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 c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2008-03-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6996 |
| _version_ | 1818386177893335040 |
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| author | Vyacheslav A. Trofimov Olga V. Matusevich |
| author_facet | Vyacheslav A. Trofimov Olga V. Matusevich |
| author_sort | Vyacheslav A. Trofimov |
| collection | DOAJ |
| description | 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.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-14T03:49:55Z |
| format | Article |
| id | doaj.art-01842ab9144748ffa59eefe1e1bcad3b |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T03:49:55Z |
| publishDate | 2008-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-01842ab9144748ffa59eefe1e1bcad3b2022-12-21T23:18:14ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102008-03-0113110.3846/1392-6292.2008.13.123-133Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearityVyacheslav A. Trofimov0Olga V. Matusevich1Lomonosov Moscow State University, Department of Computational Mathematics and Cybernetics, Leninskye Gory, 119992, Moscow, RussiaLomonosov Moscow State University, Department of Computational Mathematics and Cybernetics, Leninskye Gory, 119992, Moscow, RussiaThe 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. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/6996nonlinear Schrödinger equationseigenfunctions and eigenvalueslaser femtosecond pulsesoliton |
| spellingShingle | Vyacheslav A. Trofimov Olga V. Matusevich Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity Mathematical Modelling and Analysis nonlinear Schrödinger equations eigenfunctions and eigenvalues laser femtosecond pulse soliton |
| title | Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity |
| title_full | Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity |
| title_fullStr | Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity |
| title_full_unstemmed | Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity |
| title_short | Numerical method for 2d soliton solution at SHG in media with time‐dependent combined nonlinearity |
| title_sort | numerical method for 2d soliton solution at shg in media with time dependent combined nonlinearity |
| topic | nonlinear Schrödinger equations eigenfunctions and eigenvalues laser femtosecond pulse soliton |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6996 |
| work_keys_str_mv | AT vyacheslavatrofimov numericalmethodfor2dsolitonsolutionatshginmediawithtimedependentcombinednonlinearity AT olgavmatusevich numericalmethodfor2dsolitonsolutionatshginmediawithtimedependentcombinednonlinearity |