Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system
This article indicates one of the ways to solve the generalized Cauchy – Riemann system for quaternionic functions in an eight-dimensional space. In previous works, some classes of solutions of this system were studied and it was stated that it is possible to use the meth...
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| Format: | Article |
| Language: | English |
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Saratov State University
2023-03-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2023/02/11-23-loshkareva_et_al.pdf |
| _version_ | 1811160697805996032 |
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| author | Loshkareva, Elena Anatolievna Gladyshev, Yuri A. Malyshev, Evgeniy N. |
| author_facet | Loshkareva, Elena Anatolievna Gladyshev, Yuri A. Malyshev, Evgeniy N. |
| author_sort | Loshkareva, Elena Anatolievna |
| collection | DOAJ |
| description | This article indicates one of the ways to solve the generalized Cauchy – Riemann system for quaternionic functions in an eight-dimensional space. In previous works, some classes of solutions of this system were studied and it was stated that it is possible to use the method of generalized degrees to construct solutions of this system of differential equations. It is shown that the solution of the problem can be reduced to finding two arbitrary quaternionic harmonic functions in an eight-dimensional space. All 8 components of these functions $\varphi ,\psi$ must be harmonic functions, that is, be twice continuously differentiable over all 8 real variables $x_i$, $y_i$, where $i = \overline {1,4} $ solutions of the Laplace equation. In this article, the parametric method of generalized degrees is considered, which is applicable to individual equations of the second and higher orders. |
| first_indexed | 2024-04-10T06:01:49Z |
| format | Article |
| id | doaj.art-8fda4c85db5b459bb95f81882293302c |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-04-10T06:01:49Z |
| publishDate | 2023-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-8fda4c85db5b459bb95f81882293302c2023-03-03T07:35:06ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052023-03-01231112310.18500/1816-9791-2023-23-1-11-23Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann systemLoshkareva, Elena Anatolievna0Gladyshev, Yuri A.1Malyshev, Evgeniy N.2Kaluga State University named after K. E. Tsiolkovski, 26 Stepan Razin St., Kaluga 248023, RussiaKaluga State University named after K. E. Tsiolkovski, 26 Stepan Razin St., Kaluga 248023, RussiaBauman Moscow State Technical University (Kaluga Branch), 2 Bazhenova St., Kaluga 248000, RussiaThis article indicates one of the ways to solve the generalized Cauchy – Riemann system for quaternionic functions in an eight-dimensional space. In previous works, some classes of solutions of this system were studied and it was stated that it is possible to use the method of generalized degrees to construct solutions of this system of differential equations. It is shown that the solution of the problem can be reduced to finding two arbitrary quaternionic harmonic functions in an eight-dimensional space. All 8 components of these functions $\varphi ,\psi$ must be harmonic functions, that is, be twice continuously differentiable over all 8 real variables $x_i$, $y_i$, where $i = \overline {1,4} $ solutions of the Laplace equation. In this article, the parametric method of generalized degrees is considered, which is applicable to individual equations of the second and higher orders.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2023/02/11-23-loshkareva_et_al.pdfgeneralized bers degreesquaternioncauchy – riemann system |
| spellingShingle | Loshkareva, Elena Anatolievna Gladyshev, Yuri A. Malyshev, Evgeniy N. Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика generalized bers degrees quaternion cauchy – riemann system |
| title | Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system |
| title_full | Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system |
| title_fullStr | Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system |
| title_full_unstemmed | Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system |
| title_short | Application of the generalized degree method for constructing solutions of the quaternion variant of the Cauchy – Riemann system |
| title_sort | application of the generalized degree method for constructing solutions of the quaternion variant of the cauchy riemann system |
| topic | generalized bers degrees quaternion cauchy – riemann system |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2023/02/11-23-loshkareva_et_al.pdf |
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