Related papers: Integrability of Differential-Difference Equations…
We consider discrete probability laws on the real line, whose characteristic functions are separated from zero. In particular, this class includes arbitrary discrete infinitely divisible laws and lattice probability laws, whose…
We investigate dispersionless integrable systems in 3D associated with fourfolds in the Grassmannian Gr(3,5). Such systems appear in numerous applications in continuum mechanics, general relativity and differential geometry, and include…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
In this talk we discuss an elementary derivation of the semi-classical spectrum of neutral particles in two field theories with kink excitations. We also show that, in the non-integrable cases, each vacuum state cannot generically support…
Initial value problems for the integrable discrete equations on quad-graphs are investigated. A geometric criterion of the well-posedness of such a problem is found. The effects of the interaction of the solutions with the localized defects…
There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are: existence of negative Fuchs indices, insufficient…
Path and path deviation equations for charged, spinning and spinning charged objects in different versions of Kaluza-Klein (KK) theory using a modified Bazanski Lagrangian have been derived. The significance of motion in five dimensions,…
Based on a chain of BBGKI equations with a modified boundary condition that takes into account multiparticle correlations, kinetic equations in the approximate "pairs" collisions and in the polarization approximation, taking into account…
We show that the existence of algebraic forms of quantum, exactly-solvable, completely-integrable $A-B-C-D$ and $G_2, F_4, E_{6,7,8}$ Olshanetsky-Perelomov Hamiltonians allow to develop the {\it algebraic} perturbation theory, where…
In this work we study kink-antikink and antikink-kink collisions in hyperbolic models of fourth and sixth order. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models…
Given a number field $K$, we show that certain $K$-integral representations of closed surface groups can be deformed to being Zariski dense while preserving many useful properties of the original representation. This generalizes a method…
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo…
In this paper we introduce the notion of coalgebra symmetry for discrete systems. With this concept we prove that all discrete radially symmetric systems in standard form are quasi-integrable and that all variational discrete quasi-radially…
The spectral problem for an integrable system of particles satisfying the fusion rules of $SU(3)_k$ is expressed in terms of exact inversion identities satisfied by the commuting transfer matrices of the integrable fused $A_2^{(1)}$…
We demonstrate the existence and stability of one-dimensional (1D) topological kink configurations immersed in higher-dimensional bosonic gases and nonlinear optical setups. Our analysis pertains, in particular, to the two- and…
For kink-antikink scattering within the \phi^4 non--linear field theory in one space and one time dimension resonance type configurations emerge when the relative velocity between kink and antikink falls below a critical value. It has been…
We study kink scattering processes in the (1+1)-dimensional $\varphi^6$ model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities…
Several very interesting results connecting the theory of abelian ideals of Borel subalgebras, some ideas of D. Peterson relating the previous theory to the combinatorics of affine Weyl groups, and the theory of discrete series are stated…
A (1+1)-dimensional quantum field theory with a degenerate vacuum (in infinite volume) can contain particles, known as kinks, which interpolate between different vacua and have nontrivial restrictions on their multi-particle Hilbert space.…
We study integro-differential inclusions in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations and inclusions are covered by the…