# Creeping waves on a highly elongated body of revolution

Research output

### Abstract

Creeping waves play an important role in diffraction by a smooth convex body and give an asymptotics of the diffracted field in the shadow. Known results obtained by the boundary-layer method do not allow us to explain some of the properties of creeping waves on highly elongated bodies. In this paper, creeping waves on highly elongated bodies are studied in the case where the binormal curvature of the surface is asymptotically large. The asymptotics derived contains solutions of a differential equation of the Heun type. The analysis of the dispersion equation for the surface waves is carried out numerically. It is discovered that the magnetic creeping wave travels along the surface of a highly elongated body with much less attenuation than predicated by the usual theory.

Original language English 4149-4156 8 Journal of Mathematical Sciences 102 4 https://doi.org/10.1007/BF02673845 Published - 1 Jan 2000

### Fingerprint

Bodies of revolution
Binormal
Surface Waves
Convex Body
Attenuation
Surface waves
Diffraction
Boundary Layer
Boundary layers
Differential equations
Curvature
Differential equation

### Scopus subject areas

• Statistics and Probability
• Mathematics(all)
• Applied Mathematics

### Cite this

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title = "Creeping waves on a highly elongated body of revolution",
abstract = "Creeping waves play an important role in diffraction by a smooth convex body and give an asymptotics of the diffracted field in the shadow. Known results obtained by the boundary-layer method do not allow us to explain some of the properties of creeping waves on highly elongated bodies. In this paper, creeping waves on highly elongated bodies are studied in the case where the binormal curvature of the surface is asymptotically large. The asymptotics derived contains solutions of a differential equation of the Heun type. The analysis of the dispersion equation for the surface waves is carried out numerically. It is discovered that the magnetic creeping wave travels along the surface of a highly elongated body with much less attenuation than predicated by the usual theory.",
author = "Andronov, {I. V.}",
year = "2000",
month = "1",
day = "1",
doi = "10.1007/BF02673845",
language = "English",
volume = "102",
pages = "4149--4156",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer",
number = "4",

}

In: Journal of Mathematical Sciences , Vol. 102, No. 4, 01.01.2000, p. 4149-4156.

Research output

TY - JOUR

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AU - Andronov, I. V.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Creeping waves play an important role in diffraction by a smooth convex body and give an asymptotics of the diffracted field in the shadow. Known results obtained by the boundary-layer method do not allow us to explain some of the properties of creeping waves on highly elongated bodies. In this paper, creeping waves on highly elongated bodies are studied in the case where the binormal curvature of the surface is asymptotically large. The asymptotics derived contains solutions of a differential equation of the Heun type. The analysis of the dispersion equation for the surface waves is carried out numerically. It is discovered that the magnetic creeping wave travels along the surface of a highly elongated body with much less attenuation than predicated by the usual theory.

AB - Creeping waves play an important role in diffraction by a smooth convex body and give an asymptotics of the diffracted field in the shadow. Known results obtained by the boundary-layer method do not allow us to explain some of the properties of creeping waves on highly elongated bodies. In this paper, creeping waves on highly elongated bodies are studied in the case where the binormal curvature of the surface is asymptotically large. The asymptotics derived contains solutions of a differential equation of the Heun type. The analysis of the dispersion equation for the surface waves is carried out numerically. It is discovered that the magnetic creeping wave travels along the surface of a highly elongated body with much less attenuation than predicated by the usual theory.

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DO - 10.1007/BF02673845

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EP - 4156

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

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