Related papers: Integrability and dynamics of the Rajeev-Ranken mo…
A class of explicitly integrable models of 1+1 dimensional dilaton gravity coupled to scalar fields is described in some detail. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and…
Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed…
The stationary, axisymmetric reduction of the vacuum Einstein equations, the so-called Ernst equation, is an integrable nonlinear PDE in two dimensions. There now exists a general method for analyzing boundary value problems for integrable…
These lecture notes are a contribution to the proceedings of the school "Geometric, Algebraic and Topological Methods for Quantum Field Theory", held in Villa de Leyva, Colombia, from 31st of July to 9th of August 2023. Its intention is to…
K\"ahler's geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U($N)\otimes$U($N)$…
General properties of a class of two-dimensional dilaton gravity (DG) theories with multi-exponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is…
In this paper, we are interested in the nonlinear Rayleigh-Taylor instability for the gravity-driven incompressible Navier-Stokes equations with Navier-slip boundary conditions around a smooth increasing density profile $\rho_0(x_2)$ in a…
The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are…
Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann…
We study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of $n\times n$ systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in [47], using the…
In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral problems of the tcCH equations with $4\times4$ the Lax pair.…
We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional…
In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
In this paper we will explore the 2D system describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov's and…
In the first part of the paper, we classify linear integrable (multi-dimensionally consistent) quad-equations on bipartite isoradial quad-graphs in $\mathbb C$, enjoying natural symmetries and the property that the restriction of their…
We study the integrability of a family of birational maps obtained as reductions of the discrete Hirota equation, which are related to travelling wave solutions of the lattice KdV equation. In particular, for reductions corresponding to…
Irreversibility implies a preferred flow of time, yet special relativity denies the existence of a preferred clock. This tension has long obstructed the formulation of a relativistic master equation: standard Markovian approximations either…
We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a…
Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourgain that the 2D defocusing nonlinear Schr\"odinger equation…