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Stability of linear differential equations with a distributed delay
Exterior differential systems and prolongations for three important nonlinear partial differential equations
1. | Department of Mathematics, University of Texas, Edinburg, TX 78539, United States |
References:
[1] |
A. C. Newell, "Solitons in Mathematics and Physics,", SIAM, (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.
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.
doi: 10.1063/1.523056. |
[5] |
F. B. Estabrook, Moving frames and prolongation algebras,, J. Math. Phys., 23 (1982), 2071.
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., (1994). |
[7] |
P. Bracken, The interrelationship of integrable equations, differential geometry and the geometry of their associated surfaces,, in, (2010), 249. |
[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.
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.
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.
doi: 10.1155/IJMMS.2005.2159. |
[11] |
P. Olver, "Applications of Lie Groups to Differential Equations,", Springer-Verlag, (1993). |
[12] |
R. Camassa, D. Holm and J. Hyman, A new integrable shallow water equation,, Advances in Appl. Mechanics, 31 (1994), 1.
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.
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.
doi: 10.1103/PhysRevLett.71.1661. |
[15] |
J. Lenells, Conservation laws of the Camassa-Holm equation,, J. Phys. A: Math. Gen., 38 (2005), 869.
|
[16] |
A. Constantin and B. Kolev, Integrability of invariant metrics on the diffeomorphism group of the circle,, J. Nonlin. Sci., 16 (2006), 109.
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.
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.
doi: 10.1016/S0375-9601(99)00466-1. |
[19] |
F. B. Estabrook and H. D. Wahlquist, Prolongation structures, connection theory and Bäcklund transformation,, in, (1978). |
show all references
References:
[1] |
A. C. Newell, "Solitons in Mathematics and Physics,", SIAM, (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.
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.
doi: 10.1063/1.523056. |
[5] |
F. B. Estabrook, Moving frames and prolongation algebras,, J. Math. Phys., 23 (1982), 2071.
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., (1994). |
[7] |
P. Bracken, The interrelationship of integrable equations, differential geometry and the geometry of their associated surfaces,, in, (2010), 249. |
[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.
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.
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.
doi: 10.1155/IJMMS.2005.2159. |
[11] |
P. Olver, "Applications of Lie Groups to Differential Equations,", Springer-Verlag, (1993). |
[12] |
R. Camassa, D. Holm and J. Hyman, A new integrable shallow water equation,, Advances in Appl. Mechanics, 31 (1994), 1.
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.
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.
doi: 10.1103/PhysRevLett.71.1661. |
[15] |
J. Lenells, Conservation laws of the Camassa-Holm equation,, J. Phys. A: Math. Gen., 38 (2005), 869.
|
[16] |
A. Constantin and B. Kolev, Integrability of invariant metrics on the diffeomorphism group of the circle,, J. Nonlin. Sci., 16 (2006), 109.
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.
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.
doi: 10.1016/S0375-9601(99)00466-1. |
[19] |
F. B. Estabrook and H. D. Wahlquist, Prolongation structures, connection theory and Bäcklund transformation,, in, (1978). |
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