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Stability of solitary waves for a rod equation. (English) Zbl 1046.35094
Summary: We consider a new rod equation derived recently by H.-H. Dai [Acta Mech. 127, No. 1–4, 193–207 (1998; Zbl 0910.73036)] for a compressible hyperelastic material. We prove that the smooth solitary waves to this rod equation are orbital stable.

MSC:
35Q51 Soliton equations
35B35 Stability in context of PDEs
74H55 Stability of dynamical problems in solid mechanics
74J35 Solitary waves in solid mechanics
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