Related papers: Deriving the ADM 3+1 evolution equations from the …
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
The Lorentz transformation is derived without assuming the existence of Maxwell's equations, or that the speed of light is a constant, or even that light exists. This leads us logically to sonsider the existence of a primal field called…
By Liouville's theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement of the conformal Lie algebra which is an…
The first part of this paper develops a geometric setting for differential-difference equations that resolves an open question about the extent to which continuous symmetries can depend on discrete independent variables. For general…
Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam…
This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…
A set of infinitely many nonlocal conservation laws are revealed for (1+1)-dimensional evolution equations. For some special known integrable systems, say, the KdV and Dym equations, it is found that different nonlocal conservation laws can…
We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as…
We analyze nonlinear Schr\"odinger and wave equations whose linear part is given by the renormalized Anderson Hamiltonian in two and three dimensional periodic domains.
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the…
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. It is shown that for $H^s$ initial data, $s>-1/2$, and for any $s_1<\min(3s+1,s+1)$, the difference of the nonlinear and linear evolutions is in $H^{s_1}$…
Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form…
We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in 2+1 dimensional anti-de Sitter space in the form of some covariant constantness conditions. The infinite-dimensional representation of the anti-de…
We prove that every automorphism of an infinite-dimensional vector space over a field is the product of four involutions, a result that is optimal in the general case. We also characterize the automorphisms that are the product of three…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
We consider a natural front evolution problem the East process on $\mathbb{Z}^d, d\ge 2,$ a well studied kinetically constrained model for which the facilitation mechanism is oriented along the coordinate directions, as the equilibrium…
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on the an arbitrary background spacetime which admits ADM decomposition is discussed. We explicitly construct the…