A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of $B_n$

Alessandro Arsie; Paolo Lorenzoni; Igor Mencattini; Guglielmo Moroni

doi:10.1007/s00029-022-00804-z

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arXiv · 2111.03964

A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of $B_n$

Alessandro Arsie·Paolo Lorenzoni·Igor Mencattini·Guglielmo Moroni

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Abstract

Generalizing a construction presented in [3], we show that the orbit space of $B_2$ less the image of 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 Schr\"odinger (NLS) equations. Motivated by this example, we study the case of $B_n$ 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 $n=4$ the prepotentials we get coincide with those associated with constrained KP equations discussed in [20].

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Alessandro Arsie, Paolo Lorenzoni, Igor Mencattini, Guglielmo Moroni. 2021-11-06. A Dubrovin-Frobenius manifold structure of NLS type on the orbit space of $B_n$. https://doi.org/10.1007/s00029-022-00804-z

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