ABSTRACT
Taking into account known nonlinear solutions of nonlinear wave equations, it would be possible to assume that in the case of the finite resonators, the research of the resonant effects must lead to complex analysis and the large expressions for unknown values. However, paradoxically, it is not absolutely so. Namely, it is known that the research of nonlinear waves can be simplified at the vicinity of the resonance to the solution of the algebraic equation. Something similar takes place in different long resonators.
Since we are entering a rather complex area of researches, the great attention is paid to a comparison of theoretical and experimental results. At the same time, although the theory developed here is common to many media, data obtained for resonant waves in gas and for liquids are used with this comparison.
The evolution of waves passing through the resonant band has been studied. Effects of the quadratic nonlinearity were studied. It is found that there is a variety of waves that can be generated in the resonant band, as a result of the resonant interaction of linear, nonlinear, dispersive, and viscous effects. In particular, the wave amplitudes increase, and the wave profiles strongly change.
