Abstract
The Hirota equation is transformed into coupled nonlinear Schrödinger equations by means of the generalized perturbative reduction method. The solution of the Hirota equation is obtained for the two-component vector breather oscillating with the sum and difference frequency and wavenumbers, and this solution coincides with the vector 0π-pulse of self-induced transparency.
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REFERENCES
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Soliton Theory (Nauka, Moscow, 1980) [in Russian].
T. Taniuti and N. Iajima, J. Math. Phys. 14, 1389 (1973).
R. Hirota, The Direct Method in Soliton Theory (Cambridge Univ. Press, Cambridge, 1987).
D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, Phys. Rev. A 104, 023504 (2021). https://doi.org/10.1103/PhysRevA.104.023504
G. T. Adamashvili, Eur. Phys. J. D 74, 41 (2020). https://doi.org/10.1140/epjd/e2020-100588-y
G. T. Adamashvili, Phys. Rev. E 85, 067601 (2012). https://doi.org/10.1103/PhysRevE.85.067601
T. B. Benjamin, J. L. Bona, and J. J. Mahony, Philos. Trans. R. Soc. London, Ser. A 272, 47 (1972).
G. T. Adamashvili, Tech. Phys. Lett. 47 (2021, in press)
R. Hirota, J. Math. Phys. 14, 805 (1973).
S. V. Sazonov, Roman. Rep. Phys. 70, 401 (2018). http://www.rrp.infim.ro/IP/2018/AN401.pdf.
L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987).
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Translated by E. Oborin
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Adamashvili, G.T. The Two-Component Breather Solution of the Hirota Equation. Tech. Phys. Lett. 48, 55–57 (2022). https://doi.org/10.1134/S1063785022030014
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DOI: https://doi.org/10.1134/S1063785022030014