Abstract
A strong and hereditary symmetry operator for a multicomponent water wave equation is found which yields a hierarchy of classical symmetries. Furthermore it is shown that Eq. (3.1) possesses new symmetries which depend explicitly on the time-variablet and all of the symmetries for Eq. (3.1) form an infinitely dimensional Lie algebra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kupershmidt, B, A., Mathematics of dispersive water waves,Commun. Math. Phys.,99 (1985), 51–73.
Kupershmidt, B. A., A multicomponent water wave equation,J. Phys. A. Math. Gen.,18 (1985), 1119–1122.
Fuchssteiner, B. and Fokas, A. S., Symplectic structures, their Bäcklund transformations and hereditary symmetries,Physica D,4 (1981), 47–66.
Zhu Guocheng, Some notes about strong symmetry and hereditary symmetry,Kexue Tongbao,31 (1986), 1018–1022.
Li Yishen and Zhu Guocheng, New set of symmetries of integrable equations, Lie algebra and non-isospectral evolution equations (II), ICTP (1985), Triest.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hu, X., Li, Y. On the symmetries of a multicomponent water wave equation. Acta Mathematicae Applicatae Sinica 4, 41–45 (1988). https://doi.org/10.1007/BF02018712
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02018712