Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape
In this study, the development, design, and software implementation of the methods for solving the nonlinear diffraction problem were performed. The influence of nonlinear medium defined by the Kerr law on the propagation of a wave passing through an object was examined. The differential and integra...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-01-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/24 |
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| _version_ | 1832569175295393792 |
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| author | A. O. Lapich M. Y. Medvedik |
| author_facet | A. O. Lapich M. Y. Medvedik |
| author_sort | A. O. Lapich |
| collection | DOAJ |
| description | In this study, the development, design, and software implementation of the methods for solving the nonlinear diffraction problem were performed. The influence of nonlinear medium defined by the Kerr law on the propagation of a wave passing through an object was examined. The differential and integral formulations of the problem and the nonlinear integral equation were considered. The problem was solved for different bodies with the use of various computational grids. Convergence graphs of the iterative processes were generated. The obtained graphical results were presented. The explicit and implicit methods for solving the integral equation were compared. |
| format | Article |
| id | doaj-art-228ee669640a4229b7637adb122321f7 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-228ee669640a4229b7637adb122321f72025-02-02T23:06:08ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-01-01165210.26907/2541-7746.2023.2.167-17723Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary ShapeA. O. Lapich0M. Y. Medvedik1Penza State UniversityPenza State UniversityIn this study, the development, design, and software implementation of the methods for solving the nonlinear diffraction problem were performed. The influence of nonlinear medium defined by the Kerr law on the propagation of a wave passing through an object was examined. The differential and integral formulations of the problem and the nonlinear integral equation were considered. The problem was solved for different bodies with the use of various computational grids. Convergence graphs of the iterative processes were generated. The obtained graphical results were presented. The explicit and implicit methods for solving the integral equation were compared.https://uzakufismat.elpub.ru/jour/article/view/24integral equationscalar nonlinear diffraction problemcollocation methoditerative processnumerical method |
| spellingShingle | A. O. Lapich M. Y. Medvedik Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape Учёные записки Казанского университета: Серия Физико-математические науки integral equation scalar nonlinear diffraction problem collocation method iterative process numerical method |
| title | Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape |
| title_full | Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape |
| title_fullStr | Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape |
| title_full_unstemmed | Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape |
| title_short | Solution of a Scalar Two-Dimensional Nonlinear Diffraction Problem for Objects of Arbitrary Shape |
| title_sort | solution of a scalar two dimensional nonlinear diffraction problem for objects of arbitrary shape |
| topic | integral equation scalar nonlinear diffraction problem collocation method iterative process numerical method |
| url | https://uzakufismat.elpub.ru/jour/article/view/24 |
| work_keys_str_mv | AT aolapich solutionofascalartwodimensionalnonlineardiffractionproblemforobjectsofarbitraryshape AT mymedvedik solutionofascalartwodimensionalnonlineardiffractionproblemforobjectsofarbitraryshape |