The Theory of differential invariance and infinite dimensional Hamiltonian evolutions

Gloria Beffa

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 187-196
  • ISSN: 0137-6934

Abstract

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In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.

How to cite

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Beffa, Gloria. "The Theory of differential invariance and infinite dimensional Hamiltonian evolutions." Banach Center Publications 51.1 (2000): 187-196. <http://eudml.org/doc/209030>.

@article{Beffa2000,
abstract = {In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.},
author = {Beffa, Gloria},
journal = {Banach Center Publications},
keywords = {differential invariant; KdV evolution; Hamiltonian},
language = {eng},
number = {1},
pages = {187-196},
title = {The Theory of differential invariance and infinite dimensional Hamiltonian evolutions},
url = {http://eudml.org/doc/209030},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Beffa, Gloria
TI - The Theory of differential invariance and infinite dimensional Hamiltonian evolutions
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 187
EP - 196
AB - In this paper we describe the close relationship between invariant evolutions of projective curves and the Hamiltonian evolutions of Adler, Gel'fand and Dikii. We also show how KdV evolutions are related as well to invariant evolutions of projective surfaces.
LA - eng
KW - differential invariant; KdV evolution; Hamiltonian
UR - http://eudml.org/doc/209030
ER -

References

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  1. [1] M. Adler, On a Trace Functional for Formal Pseudo-differential Operators and the Symplectic Structure of the KdV, Inventiones Math. 50 (1979), 219-248. Zbl0393.35058
  2. [2] V. G. Drinfel'd and V. V. Sokolov, Lie Algebras and Equations of KdV Type, J. of Sov. Math. 30 (1985), 1975-2036. Zbl0578.58040
  3. [3] M. Fels and P. J. Olver Moving coframes. I. A practical algorithm, Acta Appl. Math. 51 (1998), 161-213. Zbl0937.53012
  4. [4] M. Fels and P. J. Olver Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math. 55 (1999), 127-208. Zbl0937.53013
  5. [5] I. M. Gel'fand and L. A. Dikii, A family of Hamiltonian structures connected with integrable nonlinear differential equations, in: I. M. Gelfand, Collected papers v.1, Springer-Verlag, 1987. 
  6. [6] A. González-López, R. Hernandez and G. Marí Beffa, Invariant differential equations and the Adler-Gel'fand-Dikii bracket, J. Math. Phys. 38 (1997), 5720-5738. Zbl0892.58037
  7. [7] B. A. Kupershmidt and G. Wilson, Modifying Lax equations and the second Hamiltonian structure, Inventiones Math. 62 (1981), 403-436. Zbl0464.35024
  8. [8] G. Marí Beffa, Differential invariants and KdV Hamiltonian evolutions, Bull. Soc. Math. France 127 (1999) 363-391. 
  9. [9] G. Marí Beffa and P. Olver, Differential Invariants for parametrized projective surfaces, Comm. Anal. Geom. 7 (1999), 807-839. Zbl0949.53012
  10. [10] P. Olver, Equivalence, Invariants and Symmetries, Cambridge University Press, Cambridge (1995). 
  11. [11] I. McIntosh, SL(n+1)-invariant equations which reduce to equations of Korteweg-de Vries type, Proc. of the Royal Soc. of Edinburgh 115A (1990), 367-381. Zbl0724.35095
  12. [12] E. J. Wilczynski, Projective differential geometry of curves and ruled surfaces, B.G. Teubner, Leipzig (1906). Zbl37.0620.02
  13. [13] G. Wilson, On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracket, Nonlinearity 5 (1992), 109-31. Zbl0761.58023

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