Abstract
Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.
Similar content being viewed by others
References
S. A. Akhmanov and V. E. Gusev, Sov. Phys.—Usp. 35(3), 153 (1992).
H.-Y. Hao and H. J. Maris, Phys. Rev. B: Condens. Matter 64, 064302 (2001).
J. Tucker and R. Rampton, Microwave Ultrasonics Solid State (North-Holland, Amsterdam, The Netherlands, 1971; Mir, Moscow, 1975).
V. V. Lemanov and G. A. Smolenskii, Sov. Phys.—Usp. 15(6), 708 (1973).
S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Nauka, Moscow, 1988; American Institute of Physics, New York, 1997).
T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000).
F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009).
H. Leblond and D. Mihalache, Phys. Rep. 523, 61 (2013).
F. V. Bunkin, Yu. A. Kravtsov, and G. A. Lyakhov, Sov. Phys.—Usp. 29(7), 607 (1986).
S. L. McCall and E. L. Hahn, Phys. Rev. Lett. 18, 908 (1967).
N. S. Shiren, Phys. Rev. B: Solid State 2, 2471 (1970).
G. A. Denisenko, Sov. Phys. JETP 33(6), 1215 (1971).
V. V. Samartsev, B. P. Smolyakov, and R. Z. Sharipov, JETP Lett. 20(10), 296 (1974).
V. E. Gusev and A. A. Karabutov, Laser Optoacoustics (Nauka, Moscow, 1991; American Institute of Physics, New York, 1992).
S. V. Sazonov, J. Phys.: Condens. Matter 4, 6485 (1992).
S. V. Sazonov, J. Phys.: Condens. Matter 6, 6295 (1994).
S. V. Voronkov and S. V. Sazonov, JETP 92(2), 236 (2001).
A. A. Zabolotskii, JETP 96(6), 1089 (2003).
A. A. Zabolotskii, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 67, 066606 (2003).
A. A. Zabolotskii, Physica D (Amsterdam) 185, 1239 (2003).
S. V. Sazonov and N. V. Ustinov, JETP 102(5), 741 (2006).
S. V. Sazonov and N. V. Ustinov, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 73, 056614 (2006).
A. A. Zabolotskii, JETP 105(2), 439 (2007).
S. V. Sazonov and N. V. Ustinov, Theor. Math. Phys. 151(2), 632 (2007).
S. V. Sazonov and N. V. Ustinov, J. Phys. A: Math. Gen. 40, F551 (2007).
S. V. Sazonov and N. V. Ustinov, Theor. Math. Phys. 164(2), 1016 (2010).
A. N. Bugai and S. V. Sazonov, JETP 112(3), 401 (2011).
V. A. Semenov, D. A. Dubovsky, and A. V. Orlov, Crystallogr. Rep. 56(7), 1149 (2011).
O. A. Dubovskii and A. V. Orlov, JETP Lett. 96(7), 461 (2012).
S. V. Sazonov and N. V. Ustinov, JETP 114(4), 645 (2012).
O. A. Dubovsky, V. A. Semenov, and A. V. Orlov, Phys. Solid State 55(2), 396 (2013).
V. A. Golenishchev-Kutuzov, V. V. Samartsev, N. K. Solovarov, and B. M. Khabibullin, Magnetic Quantum Acoustics (Nauka, Moscow, 1977) [in Russian].
E. Tucker, in Physical Acoustics: Principles and Methods, Ed. by W. P. Mason (Academic, New York, 1966; Mir, Moscow, 1969), Vol. 4, Part A, Chapt. 2.
E. B. Tucker, Phys. Rev. Lett. 6, 183 (1961).
C. Kittel, Phys. Rev. Lett. 6, 449 (1961).
U. Kh. Kopvillem and V. D. Korepanov, Sov. Phys. Solid State 3, 1464 (1961).
S. V. Sazonov, JETP 109(1), 57 (2009).
S. V. Sazonov, JETP 91(1), 16 (2000).
E. M. Belenov and A. V. Nazarkin, JETP Lett. 51(5), 288 (1990).
E. M. Belenov, A. V. Nazarkin, and V. A. Ushchapovskii, Sov. Phys. JETP 73(3), 422 (1991).
N. S. Buinov, V. R. Nagibarov, and N. K. Solovarov, Ukr. Fiz. Zh. 22, 151 (1977).
K. Konno, W. Kameyama, and H. J. Sanuki, J. Phys. Soc. Jpn. 37, 171 (1974).
A. M. Kosevich and A. S. Kovalev, Solid State Commun. 12, 763 (1973).
S. V. Sazonov, Phys.—Usp. 44(6), 631 (2001).
A. Scott, Active and Nonlinear Wave Propagation in Electronics (Wiley, New York, 1970; Sovetskoe Radio, Moscow, 1977).
M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. B 8, 2082 (1991).
S. K. Zhdanov and B. A. Trubnikov, Sov. Phys. JETP 65(5), 904 (1987).
S. K. Zhdanov and B. A. Trubnikov, Quasi-Gaseous Unstable Media (Nauka, Moscow, 1991) [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Volume 6: Fluid Mechanics (Nauka, Moscow, 1988; Butterworth-Heinemann, Oxford, 1989).
N. V. Karlov and N. A. Kirichenko, Vibrations, Waves, and Structures (Fizmatlit, Moscow, 2001) [in Russian].
S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, Sov. Phys.—Usp. 10(5), 609 (1967).
N. G. Vakhitov and A. A. Kolokolov, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 16, 1020 (1973).
V. E. Zakharov and E. A. Kuznetsov, Phys.—Usp. 55(6), 535 (2012).
S. V. Sazonov, Kvantovaya Elektron. 37, 29 (2007).
S. V. Sazonov, JETP 92(3), 361 (2001).
H. Leblond, S. V. Sazonov, I. V. Mel’nikov, D. Mihalache, and F. Sanchez, Phys. Rev. A: At., Mol., Opt. Phys. 74, 063815 (2006).
I. C. Eilbeck, I. D. Gibbon, P. J. Caudrey, and R. K. Bullough, J. Phys. A: Math., Nucl. Gen. 6, 1337 (1973).
Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, New York, 2003; Fizmatlit, Moscow, 2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Sazonov, 2013, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 144, No. 5, pp. 1016–1035.
Rights and permissions
About this article
Cite this article
Sazonov, S.V. On the propagation of hypersonic solitons in a strained paramagnetic crystal. J. Exp. Theor. Phys. 117, 885–902 (2013). https://doi.org/10.1134/S1063776113130062
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776113130062