Abstract
In the paper formal asymptotic solutions of the wave equation are constructed which represent concentrated wave packets propagating along rays. The construction technique is a time generalization of the frequently used spatial complex ray method. Analogously to the method of complex germ of V. P. Maslov, it is based on considering complex solutions of the Hamilton-Jacobi equation.
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Literature cited
V. P. Maslov, The Complex WKB Method in Nonlinear Equations [in Russian], Moscow (1977).
V. M. Babich and V. V. Ulin, “Complex ray solutions and eigenfunctions concentrated in a neighborhood of a closed geodesic,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,104, 6–13 (1980).
V. E. Nomofilov, “Asymptotic solutions of a system of equations of second order concentrated in a neighborhood of a ray,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,104, 170–179 (1980).
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972).
R. Courant, Partial Differential Equations [Russian translation], Moscow (1964).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 5–12, 1981.
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Babich, V.M., Ulin, V.V. Complex space-time ray method and “quasiphotons”. J Math Sci 24, 269–273 (1984). https://doi.org/10.1007/BF01086986
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DOI: https://doi.org/10.1007/BF01086986