Citation: |
[1] |
A. C. Newell, "Solitons in Mathematics and Physics," SIAM, Philadelphia, 1985. |
[2] |
M. J. Ablowitz and P. A. Clarkson, "Solitons, Nonlinear Evolution Equations and Inverse Scattering," Cambridge University Press, 1991. |
[3] |
H. D. Wahlquist and F. B. Estabrook, Prolongation structures of nonlinear evolution equations, J. Math. Phys., 16 (1975), 1-7.doi: 10.1063/1.522396. |
[4] |
H. D. Wahlquist and F. B. Estabrook, Prolongation Structures of Nonlinear Evolution Equations II, J. Math. Phys., 17 (1976), 1293-1297.doi: 10.1063/1.523056. |
[5] |
F. B. Estabrook, Moving frames and prolongation algebras, J. Math. Phys., 23 (1982), 2071-2076.doi: 10.1-63/1101.525248. |
[6] |
E. van Groesen and E. M. de Jager, "Mathematical Structures in Continuous Dynamical Systems," Studies in Math. Phys., vol. 6, North Holland, 1994. |
[7] |
P. Bracken, The interrelationship of integrable equations, differential geometry and the geometry of their associated surfaces, in "Solitary Waves in Fluid Media" (C. David and Z. Feng eds. ), Bentham Science Publishers, pgs. 249-295, (2010). |
[8] |
E. M. de Jager and S. Spannenburg, Prolongation structures and Bäcklund transformations for the matrix Korteweg-de Vries and Boomeron equation, J. Phys. A: Math. Gen., 18 (1985), 2177-2189.doi: 10.1088/0305-4470/18/12/015. |
[9] |
P. Bracken, An exterior differential system for a generalized Korteweg-de Vries equation and its associated integrability, Acta Applicandae Mathematicae, 95 (2007), 223-231.doi: 10.1007/s10440-007-9086-1. |
[10] |
P. Bracken, Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions, Int. J. Math. and Math. Sciences, 13 (2005), 2159-2173.doi: 10.1155/IJMMS.2005.2159. |
[11] |
P. Olver, "Applications of Lie Groups to Differential Equations," Springer-Verlag, New York, 1993. |
[12] |
R. Camassa, D. Holm and J. Hyman, A new integrable shallow water equation, Advances in Appl. Mechanics, 31 (1994), 1-33.doi: 10.1016/S0065-2156(08)70254-0. |
[13] |
E. G. Reyes, Geometric integrability of the Camassa-Holm equation, Lett. Math. Phys., 59 (2002), 117-131.doi: 10.1023/A:1014933316169. |
[14] |
R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Letts., 71 (1993), 1661-1664.doi: 10.1103/PhysRevLett.71.1661. |
[15] |
J. Lenells, Conservation laws of the Camassa-Holm equation, J. Phys. A: Math. Gen., 38 (2005), 869-880. |
[16] |
A. Constantin and B. Kolev, Integrability of invariant metrics on the diffeomorphism group of the circle, J. Nonlin. Sci., 16 (2006), 109-122.doi: 10.1007s00332-005-0707-4. |
[17] |
A. Hone and J. Wang, Prolongation algebras and Hamiltonian operators for peakon equations, Inverse Problems, 19 (2003), 129-145.doi: 10.1088/0266-5611/19/1/307. |
[18] |
M. Fisher and J. Schiff, The Camassa-Holm equation: conserved quantities and the initial value problem, Phys. Lett., A 259 (1999), 371-376.doi: 10.1016/S0375-9601(99)00466-1. |
[19] |
F. B. Estabrook and H. D. Wahlquist, Prolongation structures, connection theory and Bäcklund transformation, in "Nonlinear Evolution Equations Solvable by the Spectral Transform" (F. Calogero ed.), Pitman, (1978). |