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Transition to spatio-temporal chaos in the regularized long-wave equation

Abstract

During her visit, Dr. Olga Podvigina will transfer part of her experience on bifurcations in dynamical systems with symmetries through a minicourse to the Professors, post-graduation students and post-doctoral researchers of the Mathematics Department of ITA, as well as from other Departments and Institutes. This course is important for our group, since we have been studying hydromagnetic dynamos in systems with symmetries using an approach based on bifurcation theory. The course will be also useful for future exploration of simplified models of dynamo in spherical coordinates. Moreover, Dr. Podvigina will present two talks, tentatively scheduled for ITA and UNIFESP. Regarding the research activities, Dr. Podvigina will build a low-dimensional dynamical system with the same stationary states and main sequence of bifurcations as the regularized long-wave equation (RLWE), which has applications for the propagation of dynamo waves in the tachocline, where the solar dynamo is formed. She will adopt the center manifold reduction method. Our group has been regularly publishing works on the RLWE and we have observed that several dynamical transitions remain unexplained. We believe that the development of a low-dimensional model from the RLWE will help to elucidate the Physics of this important system. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
PODVIGINA, O.; ZHELIGOVSKY, V.; REMPEL, E. L.; CHIAN, A. C. -L.; CHERTOVSKIH, R.; MUNOZ, P. R. Two-parameter bifurcation study of the regularized long-wave equation. Physical Review E, v. 92, n. 3 SEP 14 2015. Web of Science Citations: 0.

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