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Solitary‐Wave Interactions in Elastic Rods

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The propagation of longitudinal deformation waves in an elastic rod is modelled by the nonlinear partial differential equation with p = 3 or 5. This equation is first derived under a range of possible constraints. We then show that this equation and even certain generalizations do not pass the PainlevĂ© test, and hence are probably not completely integrable. Finally, we study the head‐on collision of two equal solitary waves numerically and also asymptotically for small and large amplitude.
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Document Type: Research Article

Publication date: October 1, 1986

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