Geodesic
Analysis of the Bloch equations for the nuclear magnetization model
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 123-140

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We consider a system of three ordinary first-order differential equations known in the theory of nuclear magnetism as the Bloch equations. The system contains four dimensionless parameters as coefficients. Equilibrium states and the dependence of their stability on these parameters is investigated. The possibility of the appearance of two stable equilibrium states is discovered. The equations are integrable in the absence of dissipation. For the problem with small dissipation far from equilibrium, approximate solutions are constructed by the method of averaging.
Keywords: nonlinear equations, equilibrium, dissipation, stability, asymptotics, averaging. 
@article{TIMM_2012_18_2_a11,
     author = {L. A. Kalyakin},
     title = {Analysis of the {Bloch} equations for the nuclear magnetization model},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {123--140},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a11/}
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L. A. Kalyakin. Analysis of the Bloch equations for the nuclear magnetization model. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 123-140. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a11/