In solutions, which describe unfamiliar waves, were found for the disturbed wave equation. These resonant (natural or parametric resonance) waves cannot be classified as soliton- or cnoidal- or shock- or breather-type waves. Some spatiotemporally oscillating, localised, nonlinear waves have properties of both standing waves and travelling waves. The last unfamiliar waves are not the d'Alembert-type waves. Different patterns are yielded by the waves in x-t plane. The waves describe qualitatively anomalous water and granular parametric waves observed recently. Here these unfamiliar waves are studied as applied to field systems. Cavities with a vibrating boundary are considered. Methods of nonlinear acoustics are used. It is found that in the cavities the unfamiliar parametric waves can have an imagine amplitude. For this case, perhaps, these waves describe localisation and motion of a negative energy. Indeed, the generation of the negative energy density is the known result in physics (see, for instance, [5,6] ). The solutions describe a formation of particle-like waves when the dispersion reduces. An attention is focused on media with cubic nonlinearity. General cases were considered in [7].
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