Related papers: Exact solutions and automorphic systems of the geo…
A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in…
In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…
In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…
The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…
Convergence of the Gauss resolution process for a complex singular foliation of dimension r is shown to be equivalent to finite type of a graded sheaf which is built using base (r+2) expansions of integers. As applications it is calculated…
We prove automorphy lifting theorems for 2-dimensional Galois representations of absolute Galois groups of totally real fields when the residual representation is of "exceptional" type. This exceptional case is when we are in characteristic…
We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…
A family of vector fields that are the infinitesimal generators of determined one-parameter groups of transformations are constructed. It is shown that these vector fields represent symmetries of the system of differential equations…
In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…
We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
Given a finite abelian group $G$ and elements $x, y \in G$, we prove that there exists $\phi \in \text{Aut}(G)$ such that $\phi(x) = y$ if and only if $G/\langle x \rangle \cong G/\langle y \rangle$. This result leads to our development of…
We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically…
Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…
We construct extensions of the field of rational numbers with the Galois group G_2(F_p) by reducing p-adic representations attached to automorphic representations.
In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…
We look at AG codes associated to the projective line, re-examining the problem of determining their automorphism groups (originally investigated by Duer in 1987 using combinatorial techniques) using recent methods from algebraic geometry.…
The construction of the general solution sequence of row-finite linear systems is accomplished by implementing -ad infinitum- the Gauss-Jordan algorithm under a rightmost pivot elimination strategy. The algorithm generates a basis (finite…
Based on Richardson's exact solution of the pairing model and the Gaudin model for spin systems we derive a new class of exactly solvable models for finite boson system. As an example we solve a particular hamiltonian which displays a…
Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…