## 8 Citations

### Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice

- Mathematics
- 2011

### Infinite-dimensional Frobenius manifolds underlying an extension of the dispersionless Kadomtsev–Petviashvili hierarchy

- Mathematics
- 2021

### Infinite-dimensional Frobenius Manifolds Underlying the Universal Whitham Hierarchy

- Mathematics
- 2020

We construct a class of infinite-dimensional Frobenius manifolds on the spaces of pairs of meromorphic functions with a pole at infinity and a movable pole. Such Frobenius manifolds are shown to be…

### Infinite-dimensional Dubrovin-Frobenius manifolds and the Stokes phenomenon

- Mathematics
- 2022

. We study the Dubrovin equation of the inﬁnite-dimensional 2D Toda Dubrovin-Frobenius manifold at its irregular singularity. We ﬁrst revisit the deﬁnition of the canonical coordinates, proving that…

### Classical r-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics

- Mathematics
- 2015

A general scheme for the construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to Witten–Dijkgraaf–Verlinde–Verlinde associativity equations is…

### Frobenius manifolds and Frobenius algebra-valued integrable systems

- Mathematics
- 2014

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a…

### Frobenius manifolds and a new class of extended affine Weyl groups of A-type

- MathematicsLetters in Mathematical Physics
- 2020

We present a new class of extended affine Weyl groups $$\widetilde{W}^{(k,k+1)}(A_l)$$ W ~ ( k , k + 1 ) ( A l ) for $$1\le k <l$$ 1 ≤ k < l and obtain an analogue of Chevalley-type theorem for their…

## References

SHOWING 1-10 OF 28 REFERENCES

### A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds

- Mathematics
- 2011

We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion…

### Principal hierarchies of infinite-dimensional Frobenius manifolds: the extended 2D Toda lattice

- Mathematics
- 2011

### The extended bigraded Toda hierarchy

- Mathematics
- 2006

We generalize the Toda lattice hierarchy by considering N + M dependent variables. We construct roots and logarithms of the Lax operator which are uniquely defined operators with coefficients that…

### Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems

- Mathematics
- 2009

We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞, respectively.…

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

- Mathematics
- 2001

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…

### Extended affine Weyl groups and Frobenius manifolds

- MathematicsCompositio Mathematica
- 1998

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem for their…

### Frobenius Manifold for the Dispersionless Kadomtsev-Petviashvili Equation

- Mathematics
- 2010

We consider a Frobenius structure associated with the dispersionless Kadomtsev – Petviashvili equation. This is done, essentially, by applying a continuous analogue of the finite dimensional theory…

### Classical r-matrix like approach to Frobenius manifolds, WDVV equations and flat metrics

- Mathematics
- 2015

A general scheme for the construction of flat pencils of contravariant metrics and Frobenius manifolds as well as related solutions to Witten–Dijkgraaf–Verlinde–Verlinde associativity equations is…