Constantin, Adrian; Strauss, Walter A. Stability of a class of solitary waves in compressible elastic rods. (English) Zbl 1115.74339 Phys. Lett., A 270, No. 3-4, 140-148 (2000). Summary: We prove that the solitary waves of a model for nonlinear dispersive waves in cylindrical compressible hyperelastic rods are orbitally stable. This establishes that the shape of the wave is stable. Cited in 118 Documents MSC: 74J35 Solitary waves in solid mechanics 35B35 Stability in context of PDEs 35Q51 Soliton equations 74J30 Nonlinear waves in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) PDF BibTeX XML Cite \textit{A. Constantin} and \textit{W. A. Strauss}, Phys. Lett., A 270, No. 3--4, 140--148 (2000; Zbl 1115.74339) Full Text: DOI References: [2] Benjamin, B.; Bona, J.; Mahony, J., Phil. Trans. R. Soc. (London), 272, 47 (1972) [3] Camassa, R.; Holm, D., Phys. Rev. Lett., 71, 1661 (1993) [4] Constantin, A.; Escher, J., Ann. Sci. Norm. Sup. Pisa, 26, 303 (1998) [5] Constantin, A.; Escher, J., Acta Math., 181, 229 (1998) [6] Constantin, A.; McKean, H. P., Commun. Pure Appl. Math., 52, 949 (1999) [9] Dai, H.-H., Acta Mech., 127, 293 (1998) [13] Fokas, A. S.; Fuchssteiner, B., Phys. D, 4, 47 (1981) [14] Grillakis, M.; Shatah, J.; Strauss, W., J. Funct. Anal., 74, 160 (1987) [17] Souganidis, P.; Strauss, W., Proc. R. Soc. (Edinburgh), 114A, 195 (1990) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.