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On the generalizations of Bremmer series solutions of wave equations. (English) Zbl 0318.65051


MSC:

65Z05 Applications to the sciences
35C10 Series solutions to PDEs
35L05 Wave equation
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References:

[1] Bellman, R.; Vasudevan, R.; Ueno, S., On the matrix Riccati equation of transport processes, J. Math. Anal. Appl., 44, 472-481 (1973) · Zbl 0271.34026
[2] Bellman, R.; Vasudevan, R., Wave equation with sources, invariant imbedding, and Bremmer series solutions, J. Math. Anal. Appl., 48, 17-30 (1974) · Zbl 0289.34013
[3] Bremmer, H., W. K. B. approximation as the first term of the geometric optical series, (The Theory of Electromagnetic Waves Symposium (1957), Interscience: Interscience New York) · Zbl 0043.20301
[4] Wing, G. M., Invariant imbedding and generalization of the W. K. B. method and the Bremmer series, Technical Report 285 (1975)
[5] Sluijter, F. W., Generalization of the Bremmer series based on physical concepts, J. Math. Anal. Appl., 27, 282 (1969) · Zbl 0176.47101
[6] Van Kampen, N. G., Higher corrections to the W. K. B. approximation, Physica, 35, 70 (1967)
[7] Keller, H. B.; Keller, J. B., Exponential like solutions of systems of linear ordinary differential equations, J. Soc. Ind. Appl. Math., 10, 246 (1962) · Zbl 0105.28801
[8] Bakar, E., Generalized W.K.B. method with applications to problems of propagation in non-homogeneous media, J. Math. Psychol., 8, 1735 (1967)
[9] Bellman, R.; Kalaba, R., Quasilinearization and Nonlinear Boundary Value Problems (1965), American Elsevier: American Elsevier New York · Zbl 0139.10702
[10] Bellman, R.; Kalaba, R., Functional equations, wave propagation and invariant imbedding, J. Math. Mech., 8, 683 (1959) · Zbl 0090.45301
[11] Chandrasekhar, S., (Landshoff, R. K.M, Plasma in a Magnetic Field (1958), Stanford University Press: Stanford University Press Stanford, California), 14
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