Abstract
The purpose of this paper is to give a geometric description of the solitons in the principal chiral equation in 1+1 dimensions in terms of Grassmannians, and a qualitative description of their behaviour in terms of Morse functions. Additionally it shows how a soliton can be “added” to an arbitrary solution of the chiral equation.
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Beggs, E.J.: D. Phil. thesis, Oxford
Dodd, R.K., Eilbeck, J.C., Gibbon, J.D., Morris, H.C.: Solitons and nonlinear wave equations. London: Academic Press 1982
Faddeev, L.D.: A Hamiltonian interpretation of the Inverse Scattering method. Topics in current physics, vol. 17 (Solitons), pp. 339–354. Berlin, Heidelberg, New York: Springer 1980
Faddeev, L.D., Takhtajan, L.A.: Hamiltonian methods in the theory of Solitons. Berlin, Heidelberg, New York: Springer 1987
Milnor, J.: Morse theory. Annals Maths. Stud. 51 (1963)
Novikov, S., Manakov, S.V., Pitaevskii, L.P., Zakharov, V.E.: Theory of solitons. Contemporary Soviet Mathematics, Consultants Bureau 1984
Pressley, A., Segal, G.B.: Loop groups. Oxford: Oxford University Press 1988
Segal, G.B., Wilson, G.: Loop groups and equations of KdV type. Pub. Math. I.H.E.S.61, 5–65 (1985)
Uhlenbeck, K.: Harmonic maps into Lie Groups (classical solutions of the Chiral model). J. Diff. Geom.30, 1–50 (1989)
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Communicated by A. Jaffe
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Beggs, E.J. Solitons in the chiral equation. Commun.Math. Phys. 128, 131–139 (1990). https://doi.org/10.1007/BF02097049
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DOI: https://doi.org/10.1007/BF02097049