We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.
REFERENCES
1.
2.
Anand
, C. K.
, “Ward’s solitons II, exact solutions
,” Can. J. Math.
50
, 1119
(1998
).3.
Beals
, R.
and Coifman
, R. R.
, “Scattering and inverse scattering for first order systems
,” Commun. Pure Appl. Math.
37
, 39
(1984
).4.
Beals
, R.
and Coifman
, R. R.
, “Inverse scattering and evolution equations
,” Commun. Pure Appl. Math.
38
, 29
(1985
).5.
Dai
, B.
and Terng
, C. L.
, “Backlund transformations, Ward solitons, and unitons
,” J. Diff. Geom.
75
, 57
(2007
).6.
Dai
, B.
, Terng
, C. L.
, and Uhlenbeck
, K.
, “On the space-time monopole equation
,” e-print arXiv:math.DG/0602607.7.
Fokas
, A. S.
and Ioannidou
, T. A.
, “The inverse spectral theory for the Ward equation and for the chiral model
,” Commun. Pure Appl. Anal.
5
, 235
(2001
).8.
Ioannidou
, T.
, “Soliton solutions and nontrivial scattering in an integrable chiral model in dimensions
,” J. Math. Phys.
37
, 3422
(1996
).9.
Ioannidou
, T.
and Zakrzewski
, W.
, “Solutions of the modified chiral model in dimensions
,” J. Math. Phys.
39
, 2693
(1998
).10.
Pohlmeyer
, K.
, “Integrable Hamiltonian systems and interactions through quadratic constraints
,” Commun. Math. Phys.
46
, 207
(1976
).11.
Terng
, C. L.
, “Applications of Loop group factorization to geometric soliton equations
,” Proceedings of the International Congress of Mathematicians
, Madrid
, 2006
(unpublished), Vol. II
, pp. 927
–950
.12.
Terng
, C. L.
and Uhlenbeck
, K.
, “Backlund transformations and Loop group actions
,” Commun. Pure Appl. Math.
53
, 1
(2000
).13.
Uhlenbeck
, K.
, “Harmonic maps into Lie groups: Classical solutions of the chiral model
,” J. Diff. Geom.
30
, 1
(1989
).14.
Villarroel
, J.
, “The inverse problem for Ward’s system
,” Stud. Appl. Math.
83
, 211
(1990
).15.
Ward
, R. S.
, “Soliton solutions in an integrable chiral model in dimensions
,” J. Math. Phys.
29
, 386
(1988
).16.
Ward
, R. S.
, “Nontrivial scattering of localized solutions in a -dimensional integrable system
,” Phys. Lett. A
208
, 203
(1995
).17.
Wood
, J. C.
, “Explicit construction and parametrization of harmonic maps into the unitary group
,” Proc. London Math. Soc.
58
(3
), 608
(1989
).18.
Wu
, D. C.
, “The Cauchy problem of the Ward equation
,” J. Funct. Anal.
(to be published).19.
Zakharov
, V. E.
and Mikhailov
, A. V.
, “Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method
,” Sov. Phys. JETP
47
, 1017
(1978
).© 2008 American Institute of Physics.
2008
American Institute of Physics
You do not currently have access to this content.
