Integrable hierarchies and the mirror model of local CP1

@article{Brini2011IntegrableHA,
  title={Integrable hierarchies and the mirror model of local CP1},
  author={Andrea Brini and Guido Carlet and Paolo Rossi},
  journal={Physica D: Nonlinear Phenomena},
  year={2011},
  volume={241},
  pages={2156-2167}
}

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References

SHOWING 1-10 OF 59 REFERENCES

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the

ORBIFOLD QUANTUM COHOMOLOGY OF THE CLASSIFYING SPACE OF A FINITE GROUP

We work through, in detail, the quantum cohomology, with gravi- tational descendants, of the orbifold BG, the point with action of a finite group G. We provide a simple description of algebraic

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz–Ladik hierarchy

Adler and van Moerbeke (2001 Commun. Pure Appl. Math. 54 153–205) described a reduction of the 2D-Toda hierarchy called the Toeplitz lattice. This hierarchy turns out to be equivalent to the one

The spaces of Laurent polynomials, Gromov-Witten theory of ℙ1-orbifolds and integrable hierarchies

Abstract Let Mk,m be the space of Laurent polynomials in one variable , where k,m ≧ 1 are fixed integers and . According to B. Dubrovin [B. Dubrovin, Geometry of 2d topological field theories,

Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations

We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of $${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}$$, i.e., the complex projective line with a orbifold points. A

On the Structure of the Topological Phase of Two-dimensional Gravity

On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling

Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (forAn-Series): the Casimirs for the first P.B. give the
...