Geodesic
Comparative descriptions for two methods: the classical radiation method and the method of equivalent systems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 3, pp. 279-290 
É. V. Nikol'skii. Comparative descriptions for two methods: the classical radiation method and the method of equivalent systems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 3, pp. 279-290. http://geodesic.mathdoc.fr/item/SJVM_2003_6_3_a5/
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     title = {Comparative descriptions for two methods: the classical radiation method and the method of equivalent systems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the author considers two alternative methods of solution of multi-dimensional second order partial differential equations. These methods are called: the classical radiation method and the method of equivalent systems (MES). It is shown that in a sense one can consider the MES as generalization and extension of the classical radiation method. As an example the author makes use of the three-dimensional wave equation.

[1] Alekseev A. S., Gelchinskii B. Ya., “O luchevom metode vychisleniya polei voln v sluchae neodnorodnykh sred s krivolineinymi granitsami razdela”, Voprosy dinamicheskoi teorii rasprostraneniya seismicheskikh voln, Sb. III, LGU, L., 1959, 107–160

[2] Babich V. M., Buldyrev B. C., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972

[3] Babich V. M., Buldyrev B. C., Molotkov I. A., Prostranstvenno-vremennoi luchevoi metod. Lineinye i nelineinye volny, LGU, L., 1985 | MR

[4] Goldin S. V., Interpretatsiya dannykh seismicheskogo metoda otrazhennykh voln, Nauka, M., 1979

[5] Nikolskii E. V., Metod ekvivalentnykh sistem v teorii rasprostraneniya voln, Nauka. Sib. otd-nie, Novosibirsk, 1982 | MR

[6] Nikolskii E. V., Obobschennye funktsionalno-invariantnye resheniya uravnenii matematicheskoi fiziki, Izd-vo Novosibirskogo universiteta, Novosibirsk, 1995

[7] Petrashen G. I., “Elementy dinamicheskoi teorii rasprostraneniya seismicheskikh voln”, Voprosy dinamicheskoi teorii rasprostraneniya seismicheskikh voln, Sb. III, LGU, L., 1959, 11–106