Soerensen, M. P.; Christiansen, P. L.; Lomdahl, P. S. Solitary waves on nonlinear elastic rods. I. (English) Zbl 0564.73035 J. Acoust. Soc. Am. 76, 871-879 (1984). 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. Cited in 36 Documents 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 Keywords:Acoustic waves; elastic rods with circular cross section; improved Boussinesq equations; transverse motion; Solitary wave solutions; interaction between the solitary waves; numerically; nearly integrable; three conservation theorems; subsonic quasibreather; cubic nonlinearity; balance between dispersion and nonlinearity PDFBibTeX XMLCite \textit{M. P. Soerensen} et al., J. Acoust. Soc. Am. 76, 871--879 (1984; Zbl 0564.73035) Full Text: DOI Link