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首页> 外文期刊>Proceedings of the Royal Society. Mathematical, physical and engineering sciences >On chaotic wave patterns in periodically forced steady-state KdVB and extended KdVB equations
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On chaotic wave patterns in periodically forced steady-state KdVB and extended KdVB equations

机译：关于周期性强迫稳态KdVB和扩展KdVB方程中的混沌波型

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摘要

The periodically forced KdVB and extended KdVB equations are considered. We investigate the structure of the totality of steady profiles. The existence of profiles that are close to any shuffling of two basic profiles is proved, and hence the existence of spatially chaotic and recurrent solutions. The proofs are based on topological degree theory to analyse chaotic behaviour. These proofs combine ideas suggested by P. Zgliczynski (Zgliczynski 1996 Topol. Methods Nonlinear Anal. 8, 169-177) with the method of topological shadowing. The results are also applicable to the classical problem of a quite general model of a forced nonlinear oscillator with viscous damping.
机译：考虑了周期性强制KdVB和扩展KdVB方程。我们研究整体稳定结构的结构。证明了存在与两个基本轮廓的任何改组接近的轮廓，因此，存在空间混沌和递归解。证明基于拓扑度理论来分析混沌行为。这些证明结合了P. Zgliczynski（Zgliczynski 1996 Topol。Methods Nonlinear Anal。8，169-177）提出的思想和拓扑阴影法。该结果也适用于粘性阻尼强迫非线性振荡器的通用模型的经典问题。

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