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On a Nonlinear Second-Order Ordinary Differential Equation
- Authors: Kosov A.A1, Semenov E.I1
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia
- Issue: Vol 59, No 1 (2023)
- Pages: 138-141
- Section: Articles
- URL: https://rjmseer.com/0374-0641/article/view/649431
- DOI: https://doi.org/10.31857/S0374064123010120
- EDN: https://elibrary.ru/ODHRIB
- ID: 649431
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Abstract
We consider a nonlinear second-order ordinary differential equation of a special form whose particular case arises when constructing exact solutions of the nonlinear heat equation with a power-law coefficient. Conditions are obtained for the parameters under which the equation admits a single integration. A number of examples of constructing exact solutions expressed in terms of elementary functions or in terms of the Lambert function are given.
About the authors
A. A Kosov
Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia
Email: kosov_idstu@mail.ru
г. Иркутск, Россия
E. I Semenov
Matrosov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia
Author for correspondence.
Email: edwseiz@gmail.com
г. Иркутск, Россия
References
- Камке Э. Справочник по обыкновенным дифференциальным уравнениям. М., 1971.
- Косов А.А., Семенов Э.И. О точных решениях уравнения нелинейной диффузии // Сиб. мат. журн. 2019. Т. 60. № 1. С. 123-140.
- Полянин А.Д., Зайцев В.Ф. Нелинейные уравнения математической физики: в 2 ч. Ч. 1. М., 2017.
- Полянин А.Д., Зайцев В.Ф. Справочник по обыкновенным дифференциальным уравнениям. М., 2001.
- Дубинов А.Е., Дубинова И.Д., Сайков С. W-функция Ламберта и её применение в математических задачах физики. Саров, 2006.
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