科特韦格-德弗里斯方程的加速解

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-09-16 DOI:arxiv-2409.10426

Maricarmen A. Winkler, Felipe A. Asenjo

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引用次数: 0

摘要

科特韦格-德弗里斯方程是一个描述匀速孤子的基本非线性方程。相反，我们在这里证明，该方程还呈现出加速波包解。这种行为是通过将 Korteweg-de Vries 方程置于 Painlev\'e I 方程中来实现的。我们对加速波形解进行了数值探索，明确显示了它们的加速行为。

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Accelerating solutions of the Korteweg-de Vries equation

The Korteweg-de Vries equation is a fundamental nonlinear equation that describes solitons with constant velocity. On the contrary, here we show that this equation also presents accelerated wavepacket solutions. This behavior is achieved by putting the Korteweg-de Vries equation in terms of the Painlev\'e I equation. The accelerated waveform solutions are explored numerically showing their accelerated behavior explicitly.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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