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This article is cited in 13 scientific papers (total in 13 papers)
Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal
S. V. Sazonova, N. V. Ustinovb a Russian Research Centre "Kurchatov Institute"
b Tomsk State University
Abstract:
We study the interaction between longitudinal-transverse acoustic pulses and
a system of paramagnetic impurities with the effective spin $S=1$ in
a statically deformed crystal. We show that the dynamics of a pulse propagating
at an arbitrary angle to the static-deformation direction and of
the effective spins satisfy the modified reduced Maxwell–Bloch equations and, if
the spectrum of the acoustic pulse overlaps the quantum transitions between
spin sublevels, the modified sine-Gordon equation. These equations generalize
the well-known models in the theory of the inverse scattering method and in
the theory of self-induced transparency and also belong to the class of
integrable equations. Analyzing soliton solutions shows that
the pulse–medium interaction reveals some qualitatively new features in these
models compared with the cases of purely transverse or purely longitudinal
acoustic fields.
Keywords:
soliton, integrable nonlinear equation, self-induced transparency.
Received: 04.09.2006
Citation:
S. V. Sazonov, N. V. Ustinov, “Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal”, TMF, 151:2 (2007), 228–247; Theoret. and Math. Phys., 151:2 (2007), 632–647
Linking options:
https://www.mathnet.ru/eng/tmf6042https://doi.org/10.4213/tmf6042 https://www.mathnet.ru/eng/tmf/v151/i2/p228
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Abstract page: | 528 | Full-text PDF : | 196 | References: | 85 | First page: | 5 |
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