Abstract
Various procedures by which exact solutions of nonlinear equations may be used as local approximations to more general deformations are described. The theory of modulated simple waves and the Whitham/Luke description of modulations in periodic wavetrains are compared. The role of material idealisations is also discussed. Incompressibility and fibre inextensibility introduce kinematic constraints which lead to simply described deformations. These are local approximations to nearly incompressible and almost inextensible deformations.
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