Geodesic
Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 2, pp. 217-234

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This paper is concerned with a system of three nonlinear differential equations, which is a mathematical model for a system of nuclear spins in an antiferromagnet. The model has arisen in recent physical studies and differs from the well-known and well-understood Landau–Lifshitz and Bloch models in the manner of incorporating dissipation effects. It is established that the system under consideration is related to the Landau–Lifshitz system by the passage to the limit only on one invariant sphere. The initial equations contain three dimensionless parameters. Equilibrium points and their stability are examined depending on these parameters. The position of the bifurcation surface is found in the parameter space. It is proved that the corresponding equilibrium is of saddle-node type. Exact statements are illustrated by results of numerical experiments.
Keywords: nonlinear equations, equilibrium, stability
Mots-clés : bifurcation. 
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     author = {L. A. Kalyakin},
     title = {Analysis of a {Mathematical} {Model} for {Nuclear} {Spins} in an {Antiferromagnet}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {217--234},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2018_14_2_a5/}
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L. A. Kalyakin. Analysis of a Mathematical Model for Nuclear Spins in an Antiferromagnet. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 2, pp. 217-234. http://geodesic.mathdoc.fr/item/ND_2018_14_2_a5/