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The Regular and Chaotic Dynamics of Weak-Nonlinear Interaction of Waves


V.A. Buts, I.K. Kovalchuk, D.V. Tarasov, A.P. Tolstoluzhsky

In the present paper some new aspects of dynamics of weak-nonlinear interactions of waves are discussed. First of all it is shown that essential growth of the degree of the coherence of the decaying wave can be observed at three-wave interactions. The most important result is that that the part of energy of the decaying wave goes to the field of the low-frequency wave. This part of energy can be very insignificant while together with this insignificant energy all entropy practically remove from the decaying wave. The degree of the coherence of the decaying wave essentially grows in this case. The dynamics of the regimes of the decaying waves is investigated. The existence of the regime at which the degree of the coherence of the decaying packet of waves essentially grows and also regimes with chaotic dynamics is shown. The dynamics of weak-nonlinear interactions of waves in the schemes that represents practical interest is investigated. The models which appear at the description of processes in plasma when intensive laser radiation impacts on plasma and in particular the case of two laser streams (beat wave scheme) are investigated. The most interesting result of this section is that at the unlimited number of degrees of freedom (the unlimited number of interacting waves) the viewed model has the rigorous analytical solution and no complex chaotic regimes in it appear. In actual conditions the number of waves is restricted. It is shown that depending on dispersion features of medium and depending on starting conditions regimes with both regular, and with chaotic dynamics can be realized in such models. Regimes with chaotic dynamics at weak-nonlinear interaction of waves can find significant practical application. In particular they can be used for control of the spectrum characteristics of practically any generator. However, as show numerical estimations, large intensity of fields of interacting waves are in most cases necessary for practical implementation of these conditions. The magnitude of interacting waves at which the regime of the regular dynamics transfers to the chaotic regime, appears the greater the more distance between natural waves of investigated electrodynamic structure. Therefore such electrodynamic structures in which the distance between natural waves was small enough are necessary for successful implementation of chaotic regimes at the moderate values of fields. With this purpose the well known plasma model - a waveguide filled with rare plasma investigated. It is shown, that in such structure there can be fast natural waves with close values of frequencies and wave vectors.
May 29, 2020

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