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Solitary waves on nonlinear elastic rods. I. (English) Zbl 0564.73035

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.

MSC:

74J99 Waves in solid mechanics
74B20 Nonlinear elasticity
35Q99 Partial differential equations of mathematical physics and other areas of application
74J20 Wave scattering in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35L65 Hyperbolic conservation laws
35L05 Wave equation
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