On the solutions of a nonlinear 'pseudo'-oscillator equation

M Gadella; L P Lara

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On the solutions of a nonlinear 'pseudo'-oscillator equation

机译：关于非线性“伪”振动方程的解

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The second-order nonlinear equation yy″ +1=0has been proposed as a simple model to describe the dynamics of electrons in plasma physics. This equation is assumed to have periodic solutions by many authors who argue physical reasons. A great variety of approximate methods have been used in the recent literature in order to detect these periodic solutions. It is the objective of this paper to show that this equation has no periodic solutions whatsoever. In addition, the general solution can be obtained by showing that the equation is equivalent to a planar solvable Hamiltonian system.

机译：已经提出了二阶非线性方程yy''+ 1 = 0作为描述等离子体物理中电子动力学的简单模型。许多认为物理原因的作者都假定该方程具有周期解。为了检测这些周期解，最近的文献中已经使用了各种各样的近似方法。本文的目的是证明该方程没有任何周期解。另外，可以通过证明该方程等效于平面可解哈密顿系统来获得一般解。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2014年第10期|共4页
作者
M Gadella; L P Lara;
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正文语种 eng
中图分类物理学;
关键词
nonlinear equations; Hamiltonian systems; non-existence of periodic solutions;

机译：非线性方程;哈密顿系统;周期解的不存在;

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On the solutions of a nonlinear 'pseudo'-oscillator equation

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