Abstract
The criteria of integrability for the nonlinear Schrödinger-type systems are obtained. One-to-one correspondence between such integrable systems and the Jordan paris is established. It turns out that irreducible systems correspond to simple Jordan pairs. An infinite series of generalized symmetries and local conservation laws for such systems are completely described.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Mikhailov, A.V., Shabat, A.B., Yamilov, R.I.: Symmetry approach to the classification of nonlinear equations. USP. Mat. Nauk42, No. 4, 3–53 (1987)
Ablowitz, M.J.: Lectures on the inverse scattering transform. Stud. Appl. Math.108, No. 1, 17–94 (1978)
Jiber, A.V.:N-wave equation and the system of nonlinear Schrödinger equations from the group theoretical point of view. Teor. Mat. Fiz.52, No. 3, 405–413 (1982)
Fordy, A., Kulish, P.: Nonlinear Schrödinger equations and simple Lie algebras. Commun. Math. Phys.89, 427–443 (1983)
Loos, O.: Jordan pairs. Lect. Notes Math., vol. 460, p. 218. Berlin, Heidelberg, New York: Springer 1975
Bachturin, Yu.A., Slin'ko, A.M., Shestakov, I.P.: Nonassociative rings. Sov. Probl. Matem. VINITI,18, 3–72 (1981)
Loos, O.: A structure theory of Jordan pairs. Bull. Am. Math. Soc.80, No. 1, 67–71 (1974)
Mikhailov, A.V., Sokolov, V.V., Shabat, A.B.: Symmetry approach to the classification of integrable equations. In: What is integrability? Berlin, Heidelberg, New York: Springer 1991
Olver, P.: Applications of Lie groups to differential equations. Berlin, Heidelberg, New York: Springer 1986
Author information
Authors and Affiliations
Additional information
Communicated by Ya. G. Sinai
Rights and permissions
About this article
Cite this article
Svinolupov, S.I. Generalized Schrödinger equations and Jordan pairs. Commun.Math. Phys. 143, 559–575 (1992). https://doi.org/10.1007/BF02099265
Issue Date:
DOI: https://doi.org/10.1007/BF02099265