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Stability of a class of solitary waves in compressible elastic rods. (English) Zbl 1115.74339

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.

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.)
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