Related papers: On a modified Vakhnenko-Parkes equation
We consider geometric invariant theory for \emph{graded additive groups}, groups of the form $\mathbb{G}_a^r\rtimes_w\mathbb{G}_m$ such that the $\mathbb{G}_m$-action on $\mathbb{G}_a^r$ is a scalar multiplication with weight…
The coefficients of the nonlinear terms in a modified Altarelli-Parisi evolution equation with parton recombination are determined in the leading logarithmic ($Q^2$) approximation. The results are valid in the whole $x$ region and contain…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
Using the methods of the "form factor program" exact expressions of all matrix elements are obtained for several operators of the quantum sine Gordon model: all powers of the fundamental bose field, general exponentials of it, the energy…
We derive the Euler-Lagrange equation corresponding to a variant of non-Euclidean constrained von Karman theories.
We investigate compact objects in modified teleparallel gravity with realistic equations of state. We propose a modification of Teleparallel Equivalent to General Relativity, then an appropriate tetrad is applied to the field equations. A…
Recently it was discussed the Inverse Scattering Method, Part I. (paper I.) . It was a methodological Part with an example - soliton (kink) solution of the Sine-Gordon Equation. The aim of the paper I. was to introduce the Inverse…
The infinitesimal form of the induced representation of the kappa-Poincare group is constructed. The infinitesimal action of the kappa-Poincare group on the kappa-Minkowski space is described. The actions of these two infinitesimal forms on…
Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy…
We present an observation about the proposal that four-dimensional modification of general relativity may explain the observed cosmic acceleration today. Assuming that the thermodynamical nature of gravity theory continues to hold in…
The existence, uniqueness and uniformly estimates for solutions of the parameter dependent abstract Navier-Stokes problem on half space are derived. In application the existence, uniqueness and uniformly L^{p} estimates for solution of the…
We calculate the quantum vacuum interaction energy between two kinks of the sine-Gordon equation. Using the $TGTG$--formula, the problem is reduced to the known formulas for quantum fluctuations in the background of a single kink. This…
Let $\tilde\Gamma(z)$ be the modified gamma function introduced by the authors in a recent preprint "arXiv2106.14674". In this note, we obtain the following Mizuno-type result: \begin{equation*}…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations,…
We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.
The infinitesimal action of Kappa-Poincar'e group on Kappa-Minkowski space is computed both for generators of Kappa-Poincar'e algebra and those of Woronowicz generalized Lie algebra. The notion of invariant operators is introduced and…
The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years…
Let W be an irreducible, finitely generated Coxeter group. The geometric representation provides an discrete embedding in the orthogonal group of the so-called Tits form. One can look at the representation modulo the kernel of this form; we…
The sine-Gordon field theory emerges as the low-energy description in a wealth of quantum many-body systems. Recent efforts have been directed towards realizing quantum simulators of the model, by interfering two weakly coupled…