Author:
Arsie Alessandro,Lorenzoni Paolo,Mencattini Igor,Moroni Guglielmo
Abstract
AbstractGeneralizing a construction presented in Arsie and Lorenzoni (Lett Math Phys 107:1919–1961, 2017), we show that the orbit space of $$B_2$$
B
2
less the image of the coordinate lines under the quotient map is equipped with two Dubrovin-Frobenius manifold structures which are related respectively to the defocusing and the focusing nonlinear Schrödinger (NLS) equations. Motivated by this example, we study the case of $$B_n$$
B
n
and we show that the defocusing case can be generalized to arbitrary n leading to a Dubrovin-Frobenius manifold structure on the orbit space of the group. The construction is based on the existence of a non-degenerate and non-constant invariant bilinear form that plays the role of the Euclidean metric in the Dubrovin–Saito standard setting. Up to $$n=4$$
n
=
4
the prepotentials we get coincide with those associated with the constrained KP equations discussed in Liu et al. (J Geom Phys 97:177–189, 2015).
Funder
Università degli Studi di Milano - Bicocca
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
Cited by
4 articles.
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