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Solitary‐Wave Interactions in Elastic Rods
Author(s) -
Clarkson Peter A.,
LeVeque Randall J.,
Saxton Ralph
Publication year - 1986
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198675295
Subject(s) - integrable system , mathematical analysis , mathematics , amplitude , partial differential equation , nonlinear system , rod , collision , range (aeronautics) , deformation (meteorology) , physics , classical mechanics , quantum mechanics , medicine , alternative medicine , computer security , materials science , pathology , meteorology , computer science , composite material
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 Painlevé 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.