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Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. (English) Zbl 0910.73036

The analysis of the title problem is based on a set of highly nonlinear coupled equations depending on the longitudinal coordinate and time. The main progress is made by the study of the following particular cases: the linearized case which provides the existence of travelling waves of arbitrary shape, the finite-amplitude long-wave case, the far-field solution, and the finite-amplitude finite-wavelength case.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B20 Nonlinear elasticity
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