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TMF, 2007, Volume 151, Number 2, Pages 228–247 (Mi tmf6042)  

This article is cited in 10 scientific papers (total in 10 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

DOI: https://doi.org/10.4213/tmf6042

Full text: PDF file (556 kB)
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English version:
Theoretical and Mathematical Physics, 2007, 151:2, 632–647

Bibliographic databases:

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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zabolotskii A.A., “Unidirectional two-component optical pulse propagation in an isotropic two-level medium with permanent dipole moment”, Journal of Experimental and Theoretical Physics, 106:5 (2008), 846–857  crossref  adsnasa  isi  scopus
    2. Sazonov S.V., Ustinov N.V., “Propagation of picosecond transverse acoustic pulses in a Kramers doublet system”, Physics of the Solid State, 50:6 (2008), 1122–1130  crossref  adsnasa  isi  scopus
    3. Sazonov S.V., “Acoustic self-induced transparency for transverse waves in a system with resonant and quasi-resonant transitions”, Journal of Experimental and Theoretical Physics, 109:1 (2009), 57–67  crossref  adsnasa  isi  scopus
    4. S. V. Sazonov, N. V. Ustinov, “Nonlinear transparency regimes for three-component acoustic pulses in a system of electron and nuclear spins”, Theoret. and Math. Phys., 164:2 (2010), 1016–1034  mathnet  crossref  crossref  adsnasa  isi
    5. Sazonov S.V. Ustinov N.V., “Self-Induced Acoustic Transparency of Three-Component Longitudinal-Transverse Pulses”, J. Exp. Theor. Phys., 114:4 (2012), 645–653  crossref  mathscinet  adsnasa  isi  elib  scopus
    6. Sazonov S.V., “On the Propagation of Hypersonic Solitons in a Strained Paramagnetic Crystal”, J. Exp. Theor. Phys., 117:5 (2013), 885–902  crossref  adsnasa  isi  scopus
    7. S. V. Sazonov, N. V. Ustinov, “Vector acoustic solitons from the coupling of long and short waves in a paramagnetic crystal”, Theoret. and Math. Phys., 178:2 (2014), 202–222  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Sazonov S.V. Ustinov N.V., “New Integrable Model of Propagation of the Few-Cycle Pulses in An Anisotropic Microdispersed Medium”, Physica D, 366 (2018), 1–9  crossref  mathscinet  zmath  isi  scopus
    9. Sazonov V S. Ustinov V N., “Propagation of Few-Cycle Pulses in a Nonlinear Medium and An Integrable Generalization of the Sine-Gordon Equation”, Phys. Rev. A, 98:6 (2018), 063803  crossref  isi  scopus
    10. Ustinov N.V., “Integrable Generalizations of the Sine-Gordon, Short Pulse, and Reduced Maxwell-Bloch Equations”, J. Math. Phys., 60:1 (2019), 013503  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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