Summary
A remarkable relation between N-soliton solutions of theKP hierarchy and some group varieties is found. Precisely, we prove that to each such solution there is associated, in a natural way, a commutative group variety, which we are able to construct explicitly. These varieties turn out to be products of multiplicative groups.
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References
I. Barsotti,Considerazioni sulle funzioni theta, Symp. Math.,3 (1970), p. 247.
I. Barsotti,Le equazioni differenziali delle funzioni theta, Rend. Acc. Naz. XL,101 (1983), p. 227.
F. Bottacin,Group varieties related to the KPhierarchy, Ann. Mat. Pura Appl. (IV), Vol. CLXII (1992), p. 215.
E. Date -M. Jimbo -M. Kashiwara -T. Miwa,Trasformation groups for soliton equations, inProceedings RIMS Symp. Nonlinear Integrable Systems—Classical Theory and Quantum Theory (Kyoto 1981), World Scientific, Singapore (1983), p. 39.
M.Demazure - P.Gabriel,Groupes algébriques, tome I, Masson, North-Holland (1970).
G. Gerotto,Alcuni elementi di teoria degli ipercorpi, Ann. Mat. Pura Appl.,115 (1977), p. 349.
D. Mumford,Tata Lectures on Theta, vol.2, Birkhäuser, Boston-Basel-Stuttgart (1984).
T. Shiota,Characterization of Jacobian varieties in terms of soliton equations, Invent. Math.,83 (1986), p. 333.
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Bottacin, F. Explicit construction of group varieties related to soliton solutions of the KP hierarchy. Annali di Matematica pura ed applicata 164, 121–132 (1993). https://doi.org/10.1007/BF01759318
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DOI: https://doi.org/10.1007/BF01759318