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On the averaging method for rod equations with quadratic non‐linearity
Author(s) -
Buitelaar R. P.
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670170305
Subject(s) - mathematics , uniqueness , quadratic equation , method of averaging , mathematical analysis , scale (ratio) , wave equation , linearity , nonlinear system , geometry , physics , quantum mechanics
The averaging method is used to approximate solutions of systems of linearly coupled, (quadratic) non‐linear dispersive wave equations, which describe extensional–torsional dynamics of a rod. Existence and uniqueness results are established. Error estimates confirm the asymptotic validity of the approximation method on a long time‐scale. The linear couplings between the equations imply that resonance can occur inside a single mode of the solution, but energy can also be transferred to other modes.