Parabolic equation with exponential nonlinearity as the condition of joint venture linear system
An attempt is made to construct a 2 + 1 - dimensional nonlinear model that is a condition for the compatibility of a system of two first - order linear differential equations. The resulting equation is related to the operator L, A to the pair and the Lax equation, when the operator L contains differ...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
North-Caucasus Federal University
2022-09-01
|
| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/215 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850064745641541632 |
|---|---|
| author | Olesya Borisovna Surneva Olga Sergeevna Yanovskaya |
| author_facet | Olesya Borisovna Surneva Olga Sergeevna Yanovskaya |
| author_sort | Olesya Borisovna Surneva |
| collection | DOAJ |
| description | An attempt is made to construct a 2 + 1 - dimensional nonlinear model that is a condition for the compatibility of a system of two first - order linear differential equations. The resulting equation is related to the operator L, A to the pair and the Lax equation, when the operator L contains differentiation with respect to only one variable and depends parametrically on two additional variables differentiation with respect to which enters into the operator A. We study the possibility of reducing the linear part to a parabolic form, and also transformation of coordinates leading to exponential nonlinearity. The resulting equation has an applied value, since it can be attributed to Toda-type diffusion chain models, the main feature of which is the presence of nonlinearities of exponential type in them. Such equations describe the transfer of a passive impurity, for example, heat in a turbulent medium with a nonlinear turbulent thermal conductivity coeficient. |
| format | Article |
| id | doaj-art-370c4089780e41d6870d8049919ecb4e |
| institution | DOAJ |
| issn | 2308-4758 |
| language | Russian |
| publishDate | 2022-09-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Наука. Инновации. Технологии |
| spelling | doaj-art-370c4089780e41d6870d8049919ecb4e2025-08-20T02:49:13ZrusNorth-Caucasus Federal UniversityНаука. Инновации. Технологии2308-47582022-09-01016580214Parabolic equation with exponential nonlinearity as the condition of joint venture linear systemOlesya Borisovna Surneva0Olga Sergeevna Yanovskaya1North-Caucasus Federal UniversityNorth-Caucasus Federal UniversityAn attempt is made to construct a 2 + 1 - dimensional nonlinear model that is a condition for the compatibility of a system of two first - order linear differential equations. The resulting equation is related to the operator L, A to the pair and the Lax equation, when the operator L contains differentiation with respect to only one variable and depends parametrically on two additional variables differentiation with respect to which enters into the operator A. We study the possibility of reducing the linear part to a parabolic form, and also transformation of coordinates leading to exponential nonlinearity. The resulting equation has an applied value, since it can be attributed to Toda-type diffusion chain models, the main feature of which is the presence of nonlinearities of exponential type in them. Such equations describe the transfer of a passive impurity, for example, heat in a turbulent medium with a nonlinear turbulent thermal conductivity coeficient.https://scienceit.elpub.ru/jour/article/view/215олитонуравнение лаксаоператорнелинейное уравнениепара лаксауравнение в частных производныхsolitonlax equationoperatornonlinear equationlax pairpartial differential equation |
| spellingShingle | Olesya Borisovna Surneva Olga Sergeevna Yanovskaya Parabolic equation with exponential nonlinearity as the condition of joint venture linear system Наука. Инновации. Технологии олитон уравнение лакса оператор нелинейное уравнение пара лакса уравнение в частных производных soliton lax equation operator nonlinear equation lax pair partial differential equation |
| title | Parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| title_full | Parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| title_fullStr | Parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| title_full_unstemmed | Parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| title_short | Parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| title_sort | parabolic equation with exponential nonlinearity as the condition of joint venture linear system |
| topic | олитон уравнение лакса оператор нелинейное уравнение пара лакса уравнение в частных производных soliton lax equation operator nonlinear equation lax pair partial differential equation |
| url | https://scienceit.elpub.ru/jour/article/view/215 |
| work_keys_str_mv | AT olesyaborisovnasurneva parabolicequationwithexponentialnonlinearityastheconditionofjointventurelinearsystem AT olgasergeevnayanovskaya parabolicequationwithexponentialnonlinearityastheconditionofjointventurelinearsystem |