Canonically conjugate variables for the periodic Camassa-Holm equation

Nonlinearity

Volumn 18, Issue 1, 2005, Pages 415-421

  Penskoi, Alexei V ^a,b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11844251160     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/1/020     Document Type: Article

References (12)

1. Flaschka H and McLaughlin D W 1976 Canonically conjugate variables for the Korteweg-de Vries equation and the Toda lattice with periodic boundary conditions Prog. Theor. Phys. 55 438-56
2. Veselov A P and Novikov S P 1982 On Poisson brackets compatible with algebraic geometry and Korteweg-de Vries dynamics on the set of finite-zone potentials Dokl. Akad. Nauk SSSR 266 533-7 (in Russian)
3. Veselov A P and Novikov S P 1982 On Poisson brackets compatible with algebraic geometry and Korteweg-de Vries dynamics on the set of finite-zone potentials Sov. Math. Dokl. 26 357-62 (Engl. Transl.)
4. Veselov A P and Novikov S P 1984 Poisson brackets and complex tori. Algebraic geometry and its applications Tr. Math. Inst. Steklov. 165 49-61 (in Russian)
5. Krichever I M and Phong D H 1997 On the integrable geometry of soliton equations and N = 2 supersymmetric gauge theories J. Diff. Geom. 45 349-89
6. Krichever I M and Phong D H 1998 Symplectic forms in the theory of solitons Surveys in Differential Geometry: Integral Systems vol IV, ed C L Terng and K Uhlenbeck (Boston, MA: International) pp 239-313
7. Camassa R and Holm D 1993 An integrable shallow water equation with peaked solutions Phys. Rev. Lett. 71 1661-4
8. Constantin A and McKean H P 1999 A shallow water equation on the circle Commun. Pure Appl. Math. 52 949-82
9. Constantin A and Escher J 1998 Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation Commun. Pure Appl. Math. 51 475-504
10. Constantin A and Molinet L 2000 Global weak solutions for a shallow water equation Commun. Math. Phys. 21145-61
11. Alber M S, Camassa R, Fedorov Yu N, Holm D D and Marsden J E 2001 The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type Commun. Math. Phys. 221 197-227
12. Gesztesy F and Holden H 2003 Algebro-geometric solutions of the Camassa-Holm hierarchy Rev. Math. Iberoamericana 19 73-142