Geodesic
Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+
Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 163-182 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Scattering problem for two-dimensional Klein–Gordon equation with nonconstant coefficients is considered in the framework of the resolvent approach. Jost and retarded/advanced solutions and spectral data are introduced and their properties are presented. Inverse scattering problem is formulated. 
@article{TMF_1995_102_2_a0,
     author = {T. I. Garagash and A. K. Pogrebkov},
     title = {Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--182},
     year = {1995},
     volume = {102},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a0/}
}
TY  - JOUR
AU  - T. I. Garagash
AU  - A. K. Pogrebkov
TI  - Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 163
EP  - 182
VL  - 102
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a0/
LA  - ru
ID  - TMF_1995_102_2_a0
ER  - 
%0 Journal Article
%A T. I. Garagash
%A A. K. Pogrebkov
%T Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 163-182
%V 102
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a0/
%G ru
%F TMF_1995_102_2_a0
T. I. Garagash; A. K. Pogrebkov. Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+. Teoretičeskaâ i matematičeskaâ fizika, Tome 102 (1995) no. 2, pp. 163-182. http://geodesic.mathdoc.fr/item/TMF_1995_102_2_a0/

[1] Boiti M., Leon J., Martina L., Pempinelli F., Phys. Lett. A, 132 (1988), 432 | DOI | MR

[2] Boiti M., Leon J., Pempinelli F., J. Math. Phys., 31 (1990), 2612 | DOI | MR | Zbl

[3] Fokas A. S., Santini P. M., Phys. Rev. Lett., 63 (1989), 1329 | DOI | MR

[4] Fokas A. S., Santini P. M., Physica D, 44 (1990), 99 | DOI | MR

[5] Boiti M., Leon J., Pempinelli F., Inverse Problems, 3 (1987), 37–49 | DOI | MR | Zbl

[6] Garagash T. I., Pogrebkov A. K., “Resolvent method for Two–dimensional Inverse Problems”, Nonlinear evolution equations and dynamical systems, eds. Makhankov, I. Puzynin, O. Pashaev, Word. Sci., Singapore, 1992, 124–130 | MR

[7] Grinevich P. G., Manakov S. V., Funk. analiz i ego prilozh., 20:2 (1986), 14–24 | MR | Zbl

[8] Grinevich P. G., Novikov R. G., DAN SSSR, 286 (1986), 19–22 | MR | Zbl

[9] Veselov A. P., Novikov S. P., DAN SSSR, 279 (1986), 20–24 | MR

[10] Grinevich P. G., Novikov S. P., Funkts. analiz i ego prilozh., 22 (1988), 23–33 | MR | Zbl

[11] Boiti M., Leon J., Pempinelli F., Inverse Problems, 3 (1987), 371–387 | DOI | MR | Zbl

[12] Pempinelli F., Pogrebkov A. K., Polivanov M. C., Resolvent approach for the nonstationary Schrödinger equation (standard case of rapidly decreasing potential), Proc. of the 7th Workshop on Nonlinear Evolution Equations and Dynamical Systems (NEEDS'91), World Scientific Pub. Co., Singapore, 1992 | MR | Zbl

[13] Boiti M., Pempinelli F., Pogrebkov A. K., Polivanov M. C., Theor. Math. Phys., 93 (1992), 1200–1224 | DOI | MR | Zbl

[14] Boiti M., Pempinelli F., Pogrebkov A., Inverse Problems, 10 (1994), 505–519 | DOI | MR | Zbl

[15] Boiti M., Pempinelli F., Pogrebkov A., TMF, 99 (1994), 185–200 | MR | Zbl

[16] Boiti M., Pempinelli F., Pogrebkov A., “Properties of Solutions of the KPI Equation”, J. Math. Phys., 35 (1994), 4683–4718 | DOI | MR | Zbl

[17] Zhou X., SIAM J. Math. Anal., 20:4 (1989), 966–986 | DOI | MR | Zbl