Abstract
Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.
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References
V. P. Maslov, Complex Markovian Chains and Feynman Continual Integral [in Russian], Nauka, Moscow (1976).
V. P. Maslov, Sovr. Probl. Mat.,11, 153–234 (1978).
V. P. Maslov, Complex WKB-method in Nonlinear Equations [in Russian], Nauka, Moscow (1977).
M. V. Karasev and V. P. Maslov, Sovr. Probl. Mat.,13, 145–267 (1979).
M. V. Karasev and A. V. Pereskokov, Teor. Mat. Fiz.,79, No. 2, 198–208 (1989).
V. M. Babich, V. S. Buldyrev, and I. A. Molotkov, Spatiotemporal Ray-Trajectory Method. Linear and Nonlinear Waves [in Russian], Publishing House of Leningrad State University, Leningrad (1985).
I. A. Molotkov and S. A. Vakulenko, Concentrated Nonlinear Waves [in Russian], Publishing House of Leningrad State University, Leningrad (1988).
V. G. Bagrov, V. V. Belov, and A. Yu. Trifonov, in: Semiclassical Concentrated States of the Schrödinger Equation. Lecture Notes in Theoretical and Mathematical Physics, Vol. 1, Part 1 [in Russian], Kazan' (1996), pp. 15–136.
V. G. Bagrov, V. V. Belov, and A. Yu. Trifonov, Annals of Phys.,246, No. 2, 231–280 (1996).
D. N. Klyshko, Physical Principles of Quantum Electronics [in Russian], Nauka, Moscow (1986).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Transform Method [in Russian], Nauka, Moscow (1980).
H. House, Waves and Fields in Optoelectronics [Russian translation], Mir, Moscow (1988).
A. B. Nassar, Phys. Rev.,A33, No. 5, 3502–3505 (1986).
A. G. Lavkin, Yad. Fiz.,53, No. 5, 1292–1296 (1991).
V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1976).
D. Anderson, Phys. Rev.,A27, No. 6, 3135–3145 (1983).
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Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 15–23, July, 1999.
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Zhdaneev, O.V., Serezhnikov, G.N., Trifonov, A.Y. et al. Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity. Russ Phys J 42, 598–606 (1999). https://doi.org/10.1007/BF02513223
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DOI: https://doi.org/10.1007/BF02513223