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

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 Schrödinger (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].

37 pages, 1 figure

References in corpus (2)

• F-manifolds with flat structure and Dubrovin's duality
• Purely non-local Hamiltonian formalism, Kohno connections and $\vee$-systems

Cited by in corpus (2)

• Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
• Conjugate Frobenius manifold and inversion symmetry