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Conference publicationsAbstractsXX conferenceOn the modeling of the freak wavessidorovsv@mail.ru 1 pp. (accepted)On the modeling of the freak waves
Sidorov SV
Russian University of Peoples' Friendship Educational and Research Institute of Gravitation and Cosmology, Russia, 117198, Moscow, ul. Micluho-Maclay, 6. E-mail: sidorovsv@mail.ru
Wave processes play an important role in the physical, chemical, biological and other phenomena, including the socio-economic. One of the critical problems in wave processes is the formation of the so-called freak waves, which are characterized by a sudden onset, a huge amplitude, short rise and short-lived. Despite this circumstance, these waves cause catastrophic consequences: for example, in the ocean, they can lead to the destruction of ships and oil platforms in the economy - and unexpected spikes in exchange rates and shares, in a social environment - to major social unrest and possibly to the revolutionary process. As practice shows, the simulation of wave propagation using the equations of hydrodynamics can not understand the nature of the freak waves, the cause of their formation, and therefore, management of these waves. In this paper, the description of such waves is proposed to use the homoclinic solutions of nonlinear evolution equations. On the example of non-stationary Ginzburg-Landau equation, which is used to model wave propagation in active oscillating environments, it is shown that homoclinic solution of this equation describes quite well the solitary waves having the above properties. Homoclinic solution, describing a wave is represented in the phase space of a topological product of a limit cycle and a homoclinic loop. Limit cycle corresponds to oscillations of the oscillating medium, and the homoclinic loop - appearance solitary wave with a much larger amplitude than the fluctuations in the environment. Homoclinic solution exists in a fairly narrow range of the parameter space, which explains the sudden appearance of the freak waves, caused by a specific set of circumstances (parameters), and their rapid destruction. The proposed approach allows us to influence the formation and destruction of the freak waves through the system parameters of the model.
Literature. 1. Sidorov SV Travelling waves and dynamic chaos in active media. / Differential Equations, v. 45, N 2, 2009, p. 250-254.
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