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 
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/
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     title = {Scattering problem for the differential operator $\partial_x\partial_y+1+a(x,y)\partial_y+},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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