Quasi-linearization and stability analysis of some self-dual, dark equations and a new dynamical system

We describe a class of self-dual dark nonlinear dynamical systems a priori allowing their quasi-linearization, whose integrability can be effectively studied by means of a geometrically based gradient-holonomic approach. A special case of the self-dual dynamical system, parametrically dependent on a...

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Bibliographic Details
Published in:Communications in theoretical physics 2022-10, Vol.74 (10), p.105007
Main Authors: Blackmore, Denis, Prytula, Mykola M, Prykarpatski, Anatolij K
Format: Article
Language:English
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Summary:We describe a class of self-dual dark nonlinear dynamical systems a priori allowing their quasi-linearization, whose integrability can be effectively studied by means of a geometrically based gradient-holonomic approach. A special case of the self-dual dynamical system, parametrically dependent on a functional variable is considered, and the related integrability condition is formulated. Using this integrability scheme, we study a new self-dual, dark nonlinear dynamical system on a smooth functional manifold, which models the interaction of atmospheric magneto-sonic Alfvén plasma waves. We prove that this dynamical system possesses a Lax representation that allows its full direct linearization and compatible Poisson structures. Moreover, for this self-dual nonlinear dynamical system we construct an infinite hierarchy of mutually commuting conservation laws and prove its complete integrability.
ISSN:0253-6102
1572-9494
DOI:10.1088/1572-9494/ac5d28