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Theoretical investigations of linear and non-linear excitations at surfaces, interfaces and thin films

Exploitable results

The completed work exhibits a marked and sustained interest in surface waves and more particularly resonance phenomena and non-linearity (solitons, chaos) in systems which are issued either from pure elasticity or pure magnetism, or magnetoelasticity. The main aspects examined and the main results obtained concern: vibrations localised near a planar defect in a crystal, surface "solitons" on crystals, so-called "crowdions" investigated numerically, novel soliton stability problems such as the existence of a bound state moving without radiation, solitons with frequencies in the spectrum gap for diatomic chains, two-sublattice ferromagnets and anti ferromagnets, the chaotic dynamics of solitons with complex internal structure, low-frequency almost dispersionless intrinsic resonant vibrational modes in a transition layer, the resonant reflection from a sandwiched thin layer in a crystal, the progation of phase-transition fronts (localised structure) in thermoelastic ferromagnets, the non-linear duality between elastic waves (in non-linear crystals with dispersion) and quasi-particles, the modulational instability of counter-propagating waves in thin elastic layers, and wedge acoustic waves in the presence of weak dispersion. This rich variety of phenomena shows in fact a remarkable unity and opens wide horizons. The co-operants to the programme have met and thoroughly discussed their results on the occasion of a scientific meeting on the Non-linear Dynamics of Elastic Media with Microstructure in Tallinn (Estonia, May 1996; organised by the programme co-ordinator and J.Engelbrecht) of which the proceedings - containing nine contributions by the co-operants were published in the Spring 1997.

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