Invariant differential equations and the Adler-Gel'fand-Dikii bracket

Journal of Mathematical Physics

Volumn 38, Issue 11, 1997, Pages 5720-5738

  González López, Artemio ^a   Heredero, Rafael Hernández ^a   Beffa, Gloria Marí ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347703415     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532162     Document Type: Article

References (15)

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2. I. M. Gel'fand and L. A. Dikii, "A family of Hamiltonian structures connected with integrable nonlinear differential equations," in I. M. Gel'fand, Collected Papers, Vol. 1 (Springer, New York, 1987).
3. B. A. Kupershmidt and G. Wilson, "Modifying Lax equations and the second Hamiltonian structure," Invent. Math. 62, 403-36 (1981).
4. V. G. Drinfel'd and V. V. Sokolov, "Lie algebras and equations of KdV type," J. Sov. Math. 30, 1975-2036 (1985).
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6. P. J. Olver, Equivalence, Invariance and Symmetry (Cambridge University Press, Cambridge, 1995).
7. G. Wilson, "On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket," Nonlinearity 5, 109-31 (1992).
8. I. McIntosh, "SL(n + 1)-invariant equations which reduce to equations of Korteweg-de Vries type," Proc. R. Soc. Edinburgh Sect. A 115, 367-81 (1990).
9. V. Yu. Ovsienko and B. A. Khesin, "Symplectic leaves of the Gel'fand-Dikii brackets and homotopy classes of non-degenerate curves," Funct. Anal. Appl. 24, n. 1, 33-40 (1990).
10. P. J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1993), 2nd ed.
11. G.-H. Halphen, "Sur les invariants différentiels," in Euvres, Vol. 2 (Gauthier-Villars, Paris, 1913).
12. S. Lie, "Uber Differentialinvarianten," in Gesammelte Abhandlungen, Vol. 6 (B. G. Teubner, Leipzig, 1927); see M. Ackerman and R. Hermann, Sophus Lie's 1884 Differential Invariant Paper (Math Sci Press, Brookline, Mass., 1975) for an English translation.
13. S. Lie, "Uber Differentialinvarianten," in Gesammelte Abhandlungen, Vol. 6 (B. G. Teubner, Leipzig, 1927); see M. Ackerman and R. Hermann, Sophus Lie's 1884 Differential Invariant Paper (Math Sci Press, Brookline, Mass., 1975) for an English translation.
14. A. Tresse, "Sur les invariants différentiels des groupes continus de transformations," Acta Math. 18, 1-88 (1894).
15. E. J. Wilczynski, Projective Differential Geometry of Curves and Ruled Surfaces (B. G. Teubner, Leipzig, 1906).