wdvv equations
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2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
J. Vašíček ◽  
R. Vitolo

Abstract The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for N = 3. More examples in higher dimensions show that the result might hold in general. The invariance group of the bi-Hamiltonian pairs that we find for WDVV equations is the group of projective transformations. The significance of projective invariance of WDVV equations is discussed in detail. The computer algebra programs that were used for calculations throughout the paper are provided in a GitHub repository.



2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.



2021 ◽  
Vol 62 (2) ◽  
pp. 022301
Author(s):  
Richard Stedman ◽  
Ian A. B. Strachan


2021 ◽  
Vol 54 (2) ◽  
pp. 024002
Author(s):  
Maali Alkadhem ◽  
Misha Feigin
Keyword(s):  


Author(s):  
Xujia Chen

Abstract Our previous paper describes a geometric translation of the construction of open Gromov–Witten invariants by Solomon and Tukachinsky from a perspective of $A_{\infty }$-algebras of differential forms. We now use this geometric perspective to show that these invariants reduce to Welschinger’s open Gromov–Witten invariants in dimension 6, inline with their and Tian’s expectations. As an immediate corollary, we obtain a translation of Solomon–Tukachinsky’s open WDVV equations into relations for Welschinger’s invariants.



Author(s):  
Alexey Basalaev ◽  
Alexandr Buryak

Abstract A well-known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper, we present a generalization of this construction for the singularities of types $A$ and $D$ that gives a solution of the open WDVV equations. For the $A$-singularity, the resulting solution describes the intersection numbers on the moduli space of $r$-spin disks, introduced recently in a work of the 2nd author, E. Clader and R. Tessler. In the 2nd part of the paper, we describe the space of homogeneous polynomial solutions of the open WDVV equations associated to the Frobenius manifolds of finite irreducible Coxeter groups.



2019 ◽  
Vol 5 (2-3) ◽  
pp. 145-186 ◽  
Author(s):  
Alexey Basalaev ◽  
Alexandr Buryak


2019 ◽  
Vol 1194 ◽  
pp. 012061 ◽  
Author(s):  
N Kozyrev
Keyword(s):  


2017 ◽  
Vol 50 (9) ◽  
pp. 095202
Author(s):  
Ian A B Strachan ◽  
Richard Stedman
Keyword(s):  


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