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The generalized Duffing oscillator
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-09-09 , DOI: 10.1016/j.cnsns.2020.105526
Nikolay A. Kudryashov

A generalized Duffing oscillator is considered, which takes into account high-order derivatives and power nonlinearities. The Painlevé test is applied to study the integrability of the mathematical model. It is shown that the generalized Duffing oscillator passes the Painlevé test only in the case of the classic Duffing oscillator which is described by the second-order differential equation. However, in the general case there are the expansion of the general solution in the Laurent series with two arbitrary constants. This allows us to search for exact solutions of generalized Duffing oscillators with two arbitrary constants using the classical Duffing oscillator as the simplest equation. The algorithm of finding exact solutions is presented. Exact solutions for the generalized Duffing oscillator are found for equations of fourth, sixth, eighth and tenth order in the form of periodic oscillations and solitary pulse.



中文翻译:

广义Duffing振荡器

考虑了通用的Duffing振荡器,它考虑了高阶导数和功率非线性。Painlevé检验用于研究数学模型的可积性。结果表明,仅在经典的Duffing振荡器由二阶微分方程描述的情况下,广义Duffing振荡器才通过Painlevé测试。但是,在一般情况下,Laurent级数中的一般解有两个任意常数的展开。这使我们能够使用经典Duffing振荡器作为最简单的方程来搜索具有两个任意常数的广义Duffing振荡器的精确解。提出了寻找精确解的算法。针对第四,第六,

更新日期:2020-09-09
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