Abstract
The existence of indeterminacy in the choice of scattering data for the auxiliary linear system for the Davey-Stewartson I-equation is noted. A connection is established between different scattering data and the corresponding conjugation matrix for the nonlocal Riemann problem.
Similar content being viewed by others
Literature cited
L. A. Takhtadzgyan and L. D. Faddeev, Hamiltonian Approach to the Theory of Solitons [in Russian], Nauka, Moscow (1986).
A. G. Reiman and M. A. Semenov-Tyan-Shanskii, “Hamiltonian structure of Kadomtsev-Petviashvili type equations,” J. Sov. Math.,31, No. 6 (1985).
L. P. Nizhnik and M. D. Pochiniiko, “Spatially two-dimensional nonlinear Schrödinger equation as an integrable Hamiltonian system,” Preprint 85-24, Inst. Mat. Akad. Nauk USSR, Kiev (1985).
V. D. Lipovskii, “Hamiltonian structure of Kadomtsev-Petviashvili equation II in the class of decreasing Cauchy data,” Funkts. Anal. Prilozhen.,20, No. 4, 35–45 (1986).
P. P. Kulish and V. D. Lipovskii, “Hamiltonian interpretation of the method of the inverse problem for the Davey-Stewartson equation,” J. Sov. Math.,46, No. 5 (1989).
V. D. Lipovskii, “Hamiltonian approach to the Davy-Stewartson equation II,” Vestn. Leningr. Gos. Univ. (LGU), Ser. Fiz. Khim., No. 4, 67–70 (1987).
Z. Jiang, R. K. Bullough, and S. V. Manakov, “Complete integrability of the KP equations in 2+1 dimensions,” Physica D,18, 305–307 (1986).
Z. Jiang, “Integrable system and integrability,” Ph. D. thesis. Manchester UMIST, 1987.
C. L. Schultz, M. J. Ablowitz, D. Bar Yaacov, “Davey-Stewartson I — A quantum 2+1 dimensional integrable system,” Preprint, Clarkson University, Potsdam, USA, 1987.
S. V. Manakov, “The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation,” Physica D,3, 420–427 (1981).
A. S. Fokas and M. J. Ablowitz, “On the inverse scattering transform of multidimensional nonlinear equations,” J. Math. Phys.,25, 2494–2505 (1984).
L. D. Faddeev, “Inverse problem of quantum theory of scattering,” in: Current Problems of Mathematics [in Russian], Vol. 3, Vsesoyuz. Inst. Nauk. Tekh. Inform. (VINITI), Moscow (1974), pp. 93–180.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 170–175, 1987.
Rights and permissions
About this article
Cite this article
Kulish, P.P., Lipovskii, V.D. & Shirokov, A.V. Scattering data for the nonstationary Dirac equation. J Math Sci 47, 2488–2492 (1989). https://doi.org/10.1007/BF01840430
Issue Date:
DOI: https://doi.org/10.1007/BF01840430