Quasi-linearization and stability analysis of some self-dual, dark equations and a new dynamical system † † In memoriam of Boris Kupershmidt (†2010), a mathematical light in the mysterious world of ‘dark’ equations.

Document Type

Article

Publication Date

10-1-2022

Abstract

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.

Identifier

85137272101 (Scopus)

Publication Title

Communications in Theoretical Physics

External Full Text Location

https://doi.org/10.1088/1572-9494/ac5d28

ISSN

02536102

Issue

10

Volume

74

This document is currently not available here.

Share

COinS