An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber
ESAIM: Modélisation mathématique et analyse numérique, Tome 21 (1987) no. 3, pp. 405-424. 
@article{M2AN_1987__21_3_405_0,
     author = {Bamberger, Alain and Coron, Fran\c{c}ois and Ghidaglia, Jean-Michel},
     title = {An analysis of the {B.P.M.} approximation of the {Helmholtz} equation in an optical fiber},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {405--424},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {21},
     number = {3},
     year = {1987},
     mrnumber = {908238},
     zbl = {0626.65136},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1987__21_3_405_0/}
}
TY  - JOUR
AU  - Bamberger, Alain
AU  - Coron, François
AU  - Ghidaglia, Jean-Michel
TI  - An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1987
SP  - 405
EP  - 424
VL  - 21
IS  - 3
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1987__21_3_405_0/
LA  - en
ID  - M2AN_1987__21_3_405_0
ER  - 
%0 Journal Article
%A Bamberger, Alain
%A Coron, François
%A Ghidaglia, Jean-Michel
%T An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1987
%P 405-424
%V 21
%N 3
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1987__21_3_405_0/
%G en
%F M2AN_1987__21_3_405_0
Bamberger, Alain; Coron, François; Ghidaglia, Jean-Michel. An analysis of the B.P.M. approximation of the Helmholtz equation in an optical fiber. ESAIM: Modélisation mathématique et analyse numérique, Tome 21 (1987) no. 3, pp. 405-424. http://archive.numdam.org/item/M2AN_1987__21_3_405_0/

[1] A. Bamberger, F. Coron and J. M. Ghidaglia, Analyse de la B.P.M.,méthode de résolution approchée de l'équation d'Helmholtz dans une fibreoptique, modélisation, convergence et stabilité. Rapport interne de l'ÉcolePolytechnique 151, Palaiseau, France, 1986.

[2] J. T. Beale and A. Majda, Rates of convergence for viscous splitting of the Navier-Stokes équations. Math. Comput. 37, 243-260 (1981). | MR | Zbl

[3] M. D. Feit and J. A. Fleck, Light propagation in graded-index optical fibers, AppL Opt. 17, 3990-3998 (1978).

[4] R. A. Fischer and W. K. Bischel, Numerical studies of the interplay betweenself phase modulation and dispersion for intense plane wave laser puises, J.Appl. Phys. 46, 4921-4934 (1975).

[5] A. Friedman, Partial differential équations, Holt Rinehart and Winston Inc., New York, 1969. | MR | Zbl

[6] J. L. Lions, Quelques méthodes de résolution desproblèmes aux limites nonlinéaires, Dunod, Paris, 1969. | Zbl

[7] J. L. Lions and E. Magenes, Nonhomogeneous boundary value problems andapplications, Springer, Berlin, 1972 (and Dunod, Paris 1968). | Zbl

[8] L. Schwartz, Théorie des distributions, Hermann, Paris, 1966. | MR | Zbl

[9] E. Stein and G. Weiss, Fourier analysis in euclidian spaces, Princeton, 1971.

[10] R. Temam, Sur la stabilité et la convergence de la méthode des pas fractionnaires, Ann. Math. Pura. AppL LXXIV, 1968, p.191-380. | MR | Zbl