Geodesic
Asymptotic analysis of a~model of nuclear magnetic autoresonance
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 420-431

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the system of three first-order differential equations arising when averaging the Bloch equations in the theory of nuclear magnetic resonance. For the averaged system, we construct an asymptotic series for the stable solution with an infinitely increasing amplitude. This result gives a key to understanding the autoresonance in weakly dissipative magnetic systems as a phenomenon of significant growth of the magnetization initiated by a small external pumping.
Keywords: nonlinear equation, small parameter, asymptotic behavior, autoresonance, dissipation, stability.
Mots-clés : perturbation 
@article{TMF_2011_167_3_a7,
     author = {L. A. Kalyakin and O. A. Sultanov and M. A. Shamsutdinov},
     title = {Asymptotic analysis of a~model of nuclear magnetic autoresonance},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {420--431},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a7/}
}
TY  - JOUR
AU  - L. A. Kalyakin
AU  - O. A. Sultanov
AU  - M. A. Shamsutdinov
TI  - Asymptotic analysis of a~model of nuclear magnetic autoresonance
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 420
EP  - 431
VL  - 167
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a7/
LA  - ru
ID  - TMF_2011_167_3_a7
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%A O. A. Sultanov
%A M. A. Shamsutdinov
%T Asymptotic analysis of a~model of nuclear magnetic autoresonance
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 420-431
%V 167
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a7/
%G ru
%F TMF_2011_167_3_a7
L. A. Kalyakin; O. A. Sultanov; M. A. Shamsutdinov. Asymptotic analysis of a~model of nuclear magnetic autoresonance. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 420-431. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a7/