磁流体表面上的柱形Korteweg-de Vries孤子
Cylindrical Korteweg-de Vries solitons on a ferrofluid surface
摘要：
研究了载流金属丝周围磁流体圆柱体上的线性和非线性表面波。通过导线中足够大的电流的磁场抑制液柱的Rayleigh-Plateau不稳定性，轴对称表面变形在长波长极限内传播而没有色散。使用多尺度微扰理论，弱非线性区域可以由系数取决于磁场强度的Korteweg-de Vries方程描述。对于不同的电流值，因此不同的解决方案，如驼峰或孔孤子可能会产生。还阐明了在实验中观察这些结构的可能性。
英文摘要：
Linear and non-linear surface waves on a ferrofluid cylinder surrounding a current-carrying wire are investigated. Suppressing the Rayleigh-Plateau instability of the fluid column by the magnetic field of a sufficiently large current in the wire axis-symmetric surface deformations are shown to propagate without dispersion in the long wavelength limit. Using multiple scale perturbation theory the weakly non-linear regime may be described by a Korteweg-de Vries equation with coefficients depending on the magnetic field strength. For different values for the current in the wire hence different solutions such as hump or hole solitons may be generated. The possibility to observe these structures in experiments is also elucidated.
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