New non-standard Lagrangians for the Liénard-type equations

详细信息    查看全文

• 作者：Nikolai A. Kudryashov ; ^{nakudr@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Dmitry I. Sinelshchikov
• 关键词：Li&eacute ; nard-type equations ; Lagrangian ; Inverse variational problem
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：124-129
• 全文大小：512 K

文摘

Liénard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Liénard-type equations which admits a non-standard autonomous Lagrangian. As a by-product we obtain autonomous first integrals for each member of this family of equations. We also show that some of the previously known conditions for the existence of a non-standard Lagrangian for the Liénard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.