On the nonintegrability of magnetic field lines

Mahdi, Adam; Valls, Clàudìa

doi:10.1016/j.physd.2013.02.002

Physica D: Nonlinear Phenomena

2013

DOI: 10.1016/j.physd.2013.02.002

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On the nonintegrability of magnetic field lines

Adam Mahdi

Clàudìa Valls

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Cited by 2 publications

References 9 publications

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Integrability of the Hide–Skeldon–Acheson dynamo

Mahdi

Valls²

2014

Bulletin des Sciences Mathématiques

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Abstract. In this work we consider the Hide-Skeldon-Acheson dynamo modelwhere α, β, κ and λ are parameters. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. Provided α = 0 we identify the values of the parameters of this model, for which it admits a first integral. Also, as corollary of our main results we get that for α, β, κ = 0 the dynamo model does not admit a polynomial, rational or Darboux first integral.

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Integrability of the Hide–Skeldon–Acheson dynamo

Mahdi

Valls²

2014

Bulletin des Sciences Mathématiques

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On first integrals of a family of generalized Lorenz-like systems

Yang

2021

Chaos, Solitons & Fractals

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On the nonintegrability of magnetic field lines

Cited by 2 publications

References 9 publications

Integrability of the Hide–Skeldon–Acheson dynamo

Integrability of the Hide–Skeldon–Acheson dynamo

On first integrals of a family of generalized Lorenz-like systems

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