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Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction–diffusion equations with variable coefficientsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 25 апреля 2019 г.
- Автор: Polyanin A.D.
- Журнал: International Journal of Non-Linear Mechanics
- Том: 111
- Год издания: 2019
- Издательство: Pergamon Press Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 95
- Последняя страница: 105
- DOI: 10.1016/j.ijnonlinmec.2019.02.005
- Аннотация: The paper deals with different classes of non-linear reaction-diffusion equations with variable coefficients $$c(x)u_{t}=[a(x)f(u)u_x]_x+b(x)g(u),$$ that admit exact solutions. The direct method for constructing functional separable solutions to these and more complex non-linear equations of mathematical physics is described. The method is based on the representation of solutions in implicit form $$\int h(u)\,du=\xi(x)\omega(t)+\eta(x),$$ where the functions $h(u)$, $\xi(x)$, $\eta(x)$, and $\omega(t)$ are determined further by analyzing the resulting functional-differential equations. Examples of specific reaction-diffusion type equations and their exact solutions are given. The main attention is paid to non-linear equations of a fairly general form, which contain several arbitrary functions dependent on the unknown $u$ and/or the spatial variable $x$ (it is important to note that exact solutions of non-linear PDEs, that contain arbitrary functions and therefore have significant generality, are of great practical interest for testing various numerical and approximate analytical methods for solving corresponding initial-boundary value problems). Many new generalized traveling-wave solutions and functional separable solutions are described.
- Добавил в систему: Полянин Андрей Дмитриевич