Zobrazeno 1 - 10
of 300
pro vyhledávání: '"Zhang, Youjin"'
We propose a new method, which is called the tautological flow method, to analyze the integrability of partial difference equations (P$\Delta$Es) based on that of PDEs. By using this method, we prove that the discrete $q$-KdV equation is a discrete s
Externí odkaz:
http://arxiv.org/abs/2409.19530
We define a certain extension of the Ablowitz-Ladik hierarchy, and prove that this extended integrable hierarchy coincides with the topological deformation of the Principal Hierarchy of a generalized Frobenius manifold with non-flat unity.
Externí odkaz:
http://arxiv.org/abs/2404.08895
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 def
Externí odkaz:
http://arxiv.org/abs/2402.00373
For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarc
Externí odkaz:
http://arxiv.org/abs/2305.10851
For any generalized Frobenius manifold with non-flat unity, we construct a bihamiltonian integrable hierarchy of hydrodynamic type which is an analogue of the Principal Hierarchy of a Frobenius manifold. We show that such an integrable hierarchy, whi
Externí odkaz:
http://arxiv.org/abs/2209.00483
We propose two conjectural relationships between the equivariant Gromov-Witten invariants of the resolved conifold under diagonal and anti-diagonal actions and the Gromov-Witten invariants of $\mathbb{P}^1$, and verify their validity in genus zero ap
Externí odkaz:
http://arxiv.org/abs/2203.16812
For an arbitrary calibrated Frobenius manifold, we construct an infinite dimensional Lie algebra, called the Virasoro-like algebra, which is a deformation of the Virasoro algebra of the Frobenius manifold. By using the Virasoro-like algebra we give a
Externí odkaz:
http://arxiv.org/abs/2112.07526
Publikováno v:
SIGMA 18 (2022), 037, 18 pages
We construct a certain reduction of the 2D Toda hierarchy and obtain a tau-symmetric Hamiltonian integrable hierarchy. This reduced integrable hierarchy controls the linear Hodge integrals in the way that one part of its flows yields the intermediate
Externí odkaz:
http://arxiv.org/abs/2110.03317
We prove that for any tau-symmetric bihamiltonian deformation of the tau-cover of the Principal Hierarchy associated with a semisimple Frobenius manifold, the deformed tau-cover admits an infinite set of Virasoro symmetries.
Externí odkaz:
http://arxiv.org/abs/2109.01845
For any semisimple Frobenius manifold, we prove that a tau-symmetric bihamiltonian deformation of its Principal Hierarchy admits an infinite family of linearizable Virasoro symmetries if and only if all the central invariants of the corresponding def
Externí odkaz:
http://arxiv.org/abs/2109.01846