One class of solutions to the equations of ideal plasticity
Автор: Senashov S.I., Savostyanova I.L., Cherepanova O.N., Lukyanov S.V.
Журнал: Siberian Aerospace Journal @vestnik-sibsau-en
Рубрика: Informatics, computer technology and management
Статья в выпуске: 2 vol.25, 2024 года.
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Much attention is given to the study and solution of nonlinear differential equations in the modern mathematical literature. Despite this, there are not many methods for researching and solving such equations. These are point and contact transformations of equations, various methods of separating variables, the method of differential connections, the search for various symmetries and their use to construct solutions, as well as conservation laws. The paper considers a nonlinear differential equation describing the plastic flow of a prismatic rod. A group of point symmetries is found for this equation. The optimal system of onedimensional subalgebras is calculated. Conservation laws corresponding to Noetherian symmetries are given, and it is also shown that there are infinitely many non-Noetherian conservation laws. Several new invariant solutions of rank one, i. e. depending on one independent variable, are constructed. It is shown how classes of new solutions can be constructed from two exact solutions, passing to a linear equation. Thus, in this short article, almost all methods of modern research of nonlinear differential equations are involved.
Nonlinear differential equation of ideal plasticity, point symmetries, exact solutions
Короткий адрес: https://sciup.org/148329734
IDR: 148329734 | DOI: 10.31772/2712-8970-2024-25-2-182-188
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