Abstract
We construct transformation operators, which enables us to study a scattering problem and investigate the properties of a scattering operator for a multidimensional system of first-order partial differential equations.
Similar content being viewed by others
References
H. Cornille, “Multidimensional inversion formalism as a compatibility condition between different linear differential systems,”J. Phys.,12, No. 9, 1375–1398 (1979).
D. Kaup, “The inverse scattering solution for the full three-dimensional three-wave resonant interaction,”Physica 1D, No. 1, 45–67 (1980).
S. V. Manakov, “Method of the inverse scattering problem and two-dimensional evolutionary equations,”Usp. Mat. Nauk,31, No. 5, 245–246 (1976).
A. Fokas, “Inverse problem for multidimensional first-order systems,”J. Math. Phys.,27, No. 7, 1737–1746 (1986).
L. P. Nizhnik, M. D. Pochinaiko, and V. G. Tarasov, “Inverse scattering problem for a system of the Dirac equations in terms of characteristic variables,” in:Spectral Operator Theory in Problems of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983), pp. 72–93.
L. P. Nizhnik,Inverse Scattering Problems for Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1991).
L. P. Nizhnik, “The inverse scattering problem for hyperbolic equations and their application to non-linear integrable systems”Rep. Math. Phys.,26, No. 2, 261–283 (1988).
L. P. Nizhnik and V. G. Tarasov, “Multidimensional inverse scattering problem for systems of first-order partial differential equations,” in:Boundary-Value Problems for Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 84–93.
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev; Zhitomir Pedagogical Institute, Zhitomir. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1065–1076, August, 1999.
Rights and permissions
About this article
Cite this article
Nizhnik, L.P., Tarasov, V.G. Scattering problem for a multidimensional system of first-order partial differential equations. Ukr Math J 51, 1201–1213 (1999). https://doi.org/10.1007/BF02592508
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02592508