Related papers: Dispersionless Integrable Hierarchy via Kodaira-Sp…

The superintegrability of four Hamiltonians $\tilde{H_r} = \lambda\, H_r$, $r=a,b,c,d$, where $H_r$ are known Hamiltonians and $\lambda$ is a certain function defined on the configuration space and depending of a parameter $\kappa$, is…

We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian partial differential equations. Such an equation is called integrable if it can be included in an infinite…

Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogeneous Hamiltonian operators. The trios yield pairs of…

This paper defines a class of variational problems on Lie groups that admit involutive automorphisms. The maximum Principle of optimal control then identifies the appropriate left invariant Hamiltonians on the Lie algebra of the group. The…

We discuss a new covariant scalar-tensor system aimed to realise Ho\v{r}ava proposal for a power-counting renormalizable theory of gravity, with the special feature of not propagating scalar degrees of freedom in an appropriate gauge. The…

We investigate the Miura map between the dispersionless KP and dispersionless modified KP hierarchies. We show that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and…

Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key…

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case…

We show how to construct 2d field theories with holomorphic integrability from defect setups in 4d holomorphic BF. In a simple example setup, we explicitly construct the 2d theory and perform an initial classical analysis. Making use of the…

A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface…

In this article, we will construct the additional perturbative quantum torus symmetry of the dispersionless BKP hierarchy basing on the $W_{\infty}$ infinite dimensional Lie symmetry. These results show that the complete quantum torus…

This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.

This note constructs completely integrable convex Hamiltonians on the cotangent bundle of certain k-dimensional torus bundles over an l-dimensional torus. A central role is played by the Lax representation of a Bogoyavlenskij-Toda lattice.…

We propose massive gravity as a holographic framework for describing a class of strongly interacting quantum field theories with broken translational symmetry. Bulk gravitons are assumed to have a Lorentz-breaking mass term as a substitute…

We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at $0$/$\infty$ respectively, which extends the dispersionless 2D Toda…

We consider commuting operators obtained by quantization of Hamiltonians of the Hopf (aka dispersionless KdV) hierarchy. Such operators naturally arise in the setting of Symplectic Field Theory (SFT). A complete set of common eigenvectors…

We classify the Hamiltonians $H=p_x^2+p_y^2+V(x,y)$ of all classical superintegrable systems in two dimensional complex Euclidean space with second-order constants of the motion. We similarly classify the superintegrable Hamiltonians…

We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations…

Recently a new supersymmetric extension of the KdV hierarchy has appeared in a matrix-model-inspired approach to $2{-}d$ quantum supergravity. Here we prove that this hierarchy is essentially the KdV hierarchy, where the KdV field is now…

We show the complete integrability of N=2 nonstandard KP flows establishing the biHamiltonian structures. One of Hamiltonian structures is shown to be isomorphic to the nonlinear N=2 $\hat W_{\infty}$ algebra with the bosonic sector having…