We study the specific features of the evolution of spatially confined pulses with a finite amplitude and a duration of several periods of wave field oscillations both analytically and numerically. The initial equation, which describes propagation of a reflectionless ultrashort pulse, is transformed to a nonautonomous modified Korteveg-de-Vries equation after passing over to self-similar variables. In this simpler equation for the self-similar function, the dynamics of the internal structure of the wave field is determined by the competition of “dispersion” and cubic nonlinearity only. The evolution of pulses in the directions of the increasing and decreasing nonlinearity is separately considered. Numerical simulation of the problem has demonstrated that: i) the energy center of the wave packet moves nonuniformly along the propagation path, ii) a dispersion shock wave consisting of a set of solitons is excited in the rear part of a pulse propagating in the direction of increasing nonlinearity in the process of the dispersion spreading, and iii) the evolution of the pulses propagating in the direction of decreasing nonlinearity is also accompanied by excitation of a breather soliton.
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G. Z. Gareev and V.V. Luchinin, Terahertz System and Technologies (State-of-the-Art Review) [in Russian], Saint Petersburg Electrotechnical University "LETI," St. Petersburg (2015).
V. L. Bratman, A. G. Litvak, and E. V. Suvorov, Phys. Usp., 54, 837–844 (2011). https://doi.org/https://doi.org/10.3367/UFNe.0181.201108f.0867
Th.Brabec and F. Krausz, Phys. Rev. Lett., 78, No. 17, 3282–3285 (1997). https://doi.org/https://doi.org/10.1103/PhysRevLett.78.3282
E. A. Khazanov, S.Yu. Mironov, and G.Mourou, Phys. Usp., 62, 1096–1124 (2019). https://doi.org/https://doi.org/10.3367/UFNe.2019.05.038564
S.A.Akhmanov, V.A.Vysloukh, and A. S.Chirkin, Optics of Femtosecond LaserPulses, AIP, New York (1992).
E. M. Gromov and V. I.Talanov, J. Exp. Theor. Phys., 83, No. 1, 73–79 (1996).
E. M. Belenov and A. V. Nazarkin, JETP Lett., 53, No. 4, 200–203 (1991).
V. A. Mironov, J. Exp. Theor. Phys., 89, 18–23 (1999). https://doi.org/https://doi.org/10.1134/1.558949
S. A.Kozlov and S.V. Sazonov, J. Exp. Theor. Phys., 84, No. 2, 221–228 (1997). https://doi.org/https://doi.org/10.1134/1.558269
A. N. Berkovsky, S. A.Kozlov, and Y. A. Shpolyansky, Phys. Rev. A, 72, No. 4, 043821. https://doi.org/https://doi.org/10.1103/PhysRevA.72.043821
M. I.Rabinovich an D.N.Trubetskov, Oscillations and Waves: In Linear and Nonlinear Systems (Mathematics and Its Applications), Springer, Berlin (1989).
V. S. L’vov, Nonlinear Spin Waves [in Russian], Nauka, Moscow (1987).
A. A. Balakin, A. G. Litvak, V.A.Mironov, and S. A. Skobelev, J. Exp. Theor. Phys., 104, 363–378 (2007). https://doi.org/https://doi.org/10.1134/S106377610703003X
G. I. Barenblatt, Similarity, Self-Similarity, Intermediate Asymptotics [in Russian], Gidrometeoizdat, Leningrad (1982).
O.V.Rudenko and O.A. Sapozhnikov, Phys. Usp., 47, 907–922 (2004). https://doi.org/https://doi.org/10.1070/PU2004v047n09ABEH001865
A. V.Ovsyannikov, Group Analysis of Differential Equations, Academic Press (2014).
N. Kh. Ibragimov, Practical Course of Differential Equations and Mathematical Modeling [in Russian], N. I. Lobachevsky State University of Nizhny Novgorod (2007).
E. M. Lifshitz and L.P.Pitaevskii, Physical Kinetics: Vol. 10, Elsevier Science (1995).
A. M. Kamchatnov, Phys. Usp., 64, 48–82 (2021). https://doi.org/https://doi.org/10.3367/UFNe.2020.08.038815
M.A. Shamsutdinov, I.Yu. Lomakina, V.N.Nazarov et al., Ferro- and Antiferrodynamics. Nonlinear Oscillations, Waves, and Solitons [in Russian], Nauka, Moscow (2009).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 65, No. 1, pp. 35–45, January 2022. Russian DOI: https://doi.org/10.52452/00213462_2022_65_01_35
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Mironov, V.A., Fadeev, D.A. Self-Action of Ultrashort Pulses in the Self-Similar Regime. Radiophys Quantum El 65, 32–41 (2022). https://doi.org/10.1007/s11141-022-10191-2
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DOI: https://doi.org/10.1007/s11141-022-10191-2