Painlevé analysis and integrability of two-coupled non-linear oscillators

Pramana

S Rajasekar¹ 

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关键词: Two-coupled non-linear oscillators;    Painlevé analysis;    exact analytical solution.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Integrability of a linearly damped two-coupled non-linear oscillators equation egin{align*}ddot{x} & = -ddot{x} -𝛼 x -𝛿_{1}(x^{2}+y^{2})-2𝛿_{2}xy,\ddot{y} & = -ddot{y}-𝛽 y - 𝛿_{2}(x^{2}+y^{2})-2𝛿_{1}xyend{align*}is investigated by employing the Painlevé analysis. The following two integrable cases are identified:𝑑=0, 𝛼=𝛽, 𝛿1 and 𝛿2 are arbitrary.

【 授权许可】

Unknown