Solutions of the loop equations of a class of generalized Frobenius manifolds. (English) Zbl 07923628
Summary: We prove the existence and uniqueness of solution of the loop equation associated with a semisimple generalized Frobenius manifold with non-flat unity, and show, for a particular example of one-dimensional generalized Frobenius manifold, that the deformation of the Principal Hierarchy induced by the solution of the loop equation is the extended \(q\)-deformed KdV hierarchy.
MSC:
| 37Kxx | Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems |
| 53Dxx | Symplectic geometry, contact geometry |
| 81Txx | Quantum field theory; related classical field theories |
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