Peakons and coshoidal waves: Traveling wave solutions of the camassa-holm equation

Applied Mathematics and Computation

Volumn 81, Issue 2-3, 1997, Pages 173-187

  Boyd, John P ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000814560     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/0096-3003(95)00326-6     Document Type: Article

References (14)

1. R. Camassa and D. D. Holm, An Integrable Shallow Water Equation with Peaked Solitons, Phys. Rev. Lett., 71:1661-1664 (1993).
2. T. B. Benjamin, J. L. Bona, and J. Mahoney, Phil. Trans. Royal Soc. Lond. A327, 47 (1972).
3. R. Camassa, D. D. Holm, and J. M. Hyman, A new integrable shallow water equation, in Advances in Applied Mechanics 31 (T.-Y. Wu and J. W. Hutchinson, Eds.), Academic, pp. 1-33, 1994.
4. F. Cooper and H. Shepard, Solitons in the Camassa-Holm Shallow Water Equation. To be published.
5. J. P. Boyd, Weakly Nonlocal Solitons for Capillary-Gravity Waves: Fifth-degree Korteweg-deVries Equation, Physica D48, 129-146 (1991).
6. J. P. Boyd, Weakly Nonlocal Solitary Waves and Other Exponentially Small Phenomena, Cambridge University Press, New York (1995).
7. J. P. Boyd, Solitons From Sine Waves: Analytical and Numerical Methods for Nonintegrable Solitary and Cnoidal Waves, Physica D21, 227-246 (1986).
8. M. J. Lighthill, An Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press, New York.
9. J. P. Boyd, New directions in solitons and nonlinear periodic waves: polycnoidal waves, imbricated solitons, weakly non-local solitary waves and numerical boundary value algorithms, in Advances in Applied Mechanics, 27 (T.-Y. Wu and J. W. Hutchinson, Eds.), Academic, New York, pp. 1-82, 1989.
10. A. Parker, Periodic solutions of the intermediate long-wave equation: A nonlinear superposition principle. J. Math. Phys. A25:2005-2032 (1992).
11. K. W. Chow, Theta functions and dispersion relations of periodic waves. J. Phys. Soc. Japan 62:2007-2011 (1993).
12. J. P. Boyd and S. E. Haupt, Polycnoidal waves: Spatially periodic generalizations of multiple solitary waves. In Nonlinear Topics of Ocean Physics: Fermi Summer School, Course LIX (A. R. Osborne, Ed.) North-Holland, Amsterdam, 1991, pp. 827-856.
13. A. Parker, On the periodic solution of the Burgers equation: A unified approach. Proc. R. Soc. London A438:113-132 (1992).
14. J. P. Boyd, The arctan/tan and Kepler-Burger mappings for periodic solutions i with a shock, front, or internal boundary layer. J. Comp. Phys., 98:181-193 (1992).