Solitary waves on nonlinear elastic rods. I

Mads Peter Sørensen; Peter Leth Christiansen; P. S. Lomdahl

doi:10.1121/1.391312

Solitary waves on nonlinear elastic rods. I

Mads Peter Sørensen, Peter Leth Christiansen, P. S. Lomdahl

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Abstract

Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.

Original language	English
Journal	Acoustical Society of America. Journal
Volume	76
Issue number	3
Pages (from-to)	871-879
ISSN	0001-4966
DOIs	https://doi.org/10.1121/1.391312
Publication status	Published - 1984

Bibliographical note

Copyright (1984) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

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10.1121/1.391312

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http://dx.doi.org/10.1121/1.391312

Cite this

Sørensen, M. P., Christiansen, P. L., & Lomdahl, P. S. (1984). Solitary waves on nonlinear elastic rods. I. Acoustical Society of America. Journal, 76(3), 871-879. https://doi.org/10.1121/1.391312

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AU - Christiansen, Peter Leth

AU - Lomdahl, P. S.

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N2 - Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.

AB - Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.

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DO - 10.1121/1.391312

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JF - Acoustical Society of America. Journal

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