Characteristics and the initial value problem of a completely integrable shallow water equation

Discrete and Continuous Dynamical Systems - Series B

Volumn 3, Issue 1, 2003, Pages 115-139

  Camassa, Roberto ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Completely integrable systems; Hamiltonian structures; Lattice dynamics

Indexed keywords

EID: 0041760859     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2003.3.115     Document Type: Article

References (13)

1. [1] R. Beals, D.H. Sattinger, J. Szmigielski [1999], Multi-peakons and a theorem of Stietjes, Inverse Problems 15 L1-L4.
2. T.B. Benjamin, J.L. Bona and J.J. Mahoney, [1972]. Model equations for long waves in nonlinear dispersive systems, Phil. Trans. Roy. Soc. A 227 47-78.
3. F. Calogero and J.-P. Francoise, [1996]. A completely integrable Hamiltonian system, J. Math. Phys. 37 2863-2871.
4. R. Camassa and D.D. Holm, [1993]. An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 1661-1665.
5. R. Camassa, D.D. Holm, and J.M. Hyman, [1994]. A new integrable shallow water equation. Advan. Appl. Mech. 31 1-33.
6. R. Camassa, and A.I. Zenchuk, [2001]. On the initial value problem for a completely integrable shallow water wave equation. Phys. Lett. A 281 26-33.
7. U. Grenader and G. Szego, Toeplitz Forms and Their Applications, University of California Press, Berkeley and Los Angeles, 1958.
8. J.K. Hunter and Y.X. Zheng, [1994]. On a completely integrable nonlinear hyperbolic variational equation. Physica D 79, 361-386.
9. Y. Kodama and K.T-R McLaughlin, [1996]. Explicit integration of the full symmetric Toda hierarchy and the sorting property, Lett. Math. Phys. 37 37-47.
10. J. Moser, [1975]. Finitely many mass points on the line interacting under the influence of an exponential potential - an integrable system, Lecture Notes in Physics 38 467-497.
11. O. Ragnisco and M. Bruschi, [1996]. Peakons, r-matrix and Toda lattice, Physica A 228 150-159.
12. P. Rosenau, [1994]. Nonlinear dispersion and compact structures, Phys. Rev. Lett. 73 1737-1740.
13. F.G. Tricomi, Integral Equations Dover, New York, 1984.