Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem that allows analytic investigation of the statistical distribution of the contact force magnitude. A toy model of the Boltzmann-type equation for the contact force distribution probability is formulated and studied. An experimentally observed exponential distribution is derived. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We study an equation with periodically distributed delay. The dependence of the equilibrium state stability on the parameters is investigated. We show that the stability region can have a complicated shape. For a long delay, we construct the asymptotic approximations of expressions for the stability region boundary in the parameter space. We construct the normal forms and determine the occurring bifurcations in the critical cases. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider special systems of ordinary differential equations, the so-called fully coupled networks of nonlinear oscillators. For a given class of systems, we propose methods that allow examining problems of the existence and stability of periodic two-cluster synchronization modes. For any of these modes, the set of oscillators falls into two disjoint classes. Within these classes, complete synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We study automorphisms of a \(6\) -torus with one-dimensional stable and unstable manifolds, and a four-dimensional center manifold. Such automorphisms are generated by integer matrices and are symplectic with respect to either the standard symplectic structure on \(\mathbb{R}^6\) or a nonstandard symplectic structure generated by an integer skew-symmetric nondegenerate matrix. Such a symplectic matrix generates a partially hyperbolic automorphism of the torus if its eigenvalues are given by a pair of real numbers outside the unit circle and two pairs of conjugate complex numbers on the unit circle. The classification is determined by the topology of a foliation generated by unstable (stable) leaves of the automorphism and its action on the center manifold. There are two different cases, transitive and decomposable ones. In the first case, the foliation into unstable (stable) leaves is transitive, and in the second case, the foliation itself has a subfoliation into \(2\) -dimensional or \(4\) -dimensional tori. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider a boundary value problem based on a logistic model with delay and diffusion describing the dynamics of changes in the population density in a planar domain. It has spatially inhomogeneous stable solutions branching off from a spatially homogeneous solution and sharing qualitatively the same dynamical properties. We numerically investigate their phase bifurcations with a significant decrease in the diffusion coefficient. The coexisting stable modes with qualitatively different properties are also constructed numerically. Based on the applied numerical and analytic methods, the solutions of the considered boundary value problem are divided into two types, the first of which includes solutions that inherit the properties of the homogeneous solution and the second includes the so-called self-organization modes. Solutions of the second type are more intricately distributed in space and have properties much more preferable from the standpoint of population dynamics. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The quasipolynomial (QP) formalism and the Painlevé property constitute two distinct approaches for studying the integrability of systems of ordinary differential equations with polynomial nonlinearities. The former relies on a set of quasimonomial variable transformations, which explore the existence of hidden quasipolynomial invariants, while the latter requires that all solutions be meromorphic, expressed in the form of Laurent series in the complex time domain. In this paper, we compare the effectiveness of these approaches as independent methods for identifying integrals of motion, in many examples of polynomial dynamical systems of physical interest. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider a singularly perturbed periodic problem for a Burgers-type equation with modular advection and periodic linear amplification. We obtain conditions for the existence, uniqueness, and asymptotic stability in the sense of Lyapunov of a periodic solution with an interior transition layer and construct its asymptotic approximation. The asymptotics of the solution is used to determine boundary conditions ensuring the implementation of a prescribed mode of the front motion, i.e., the boundary control problem. We also formulate the notion of an asymptotic solution of the boundary control problem and obtain sufficient conditions for the existence of the required periodic mode of the front motion. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The \(b\) -family is a one-parameter family of Hamiltonian partial differential equations of nonevolutionary type, which arises in shallow water wave theory. It admits a variety of solutions, including the celebrated peakons, which are weak solutions in the form of peaked solitons with a discontinuous first derivative at the peaks, as well as other interesting solutions that have been obtained in exact form and/or numerically. In each of the special cases \(b=2\) and \(b=3\) (the Camassa–Holm and Degasperis–Procesi equations, respectively), the equation is completely integrable, in the sense that it admits a Lax pair and an infinite hierarchy of commuting local symmetries, but for other values of the parameter \(b\) it is nonintegrable. After a discussion of traveling waves via the use of a reciprocal transformation, which reduces to a hodograph transformation at the level of the ordinary differential equation satisfied by these solutions, we apply the same technique to the scaling similarity solutions of the \(b\) -family and show that when \(b=2\) or \(b=3\) , this similarity reduction is related by a hodograph transformation to particular cases of the Painlevé III equation, while for all other choices of \(b\) the resulting ordinary differential equation is not of Painlevé type. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: This paper is devoted to tetrahedron maps, which are set-theoretical solutions of the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron maps on associative rings. The obtained maps are new to our knowledge. We show that matrix tetrahedron maps derived previously are a particular case of our construction. This provides an algebraic explanation of the fact that the matrix maps satisfy the tetrahedron equation. Also, Liouville integrability is established for some of the constructed maps. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: The paper is devoted to real Hamiltonian forms of \(2\) -dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of “reductions ” of Hamiltonian systems, similar to real forms of semisimple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac–Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann–Hilbert problems and derive the minimal sets of scattering data that uniquely determine the scattering matrices and the potentials of the Lax operators. PubDate: 2022-08-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We describe an explicit formula for the first-order quasiderivation of an arbitrary central element of the universal enveloping algebra of a general linear Lie algebra. We apply it to show that derivations of any two central elements of the universal enveloping algebra commute. This contributes to the Vinberg problem of finding commutative subalgebras in universal enveloping algebras with the underlying Poisson algebras determined by the argument shift method. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We discuss the properties of second-order Killing tensors in three-dimensional Euclidean space that guarantee the existence of a third integral of motion ensuring the Liouville integrability of the corresponding equations of motion. We prove that in addition to the linear Noether and quadratic Stäckel integrals of motion, there are integrable systems with two quadratic integrals of motion and one fourth-order integral of motion in momenta. A generalization to \(n\) -dimensional case and to deformations of the standard flat metric is proposed. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: A generalized model of Hamiltonian mechanics is considered. It includes two special cases: a model of the dynamics of three magnetic vortices in ferromagnets and a model of the dynamics of three hydrodynamic vortices in a perfect fluid. A constraint is imposed on the system by fixing one of the vortices at the point of origin. The system of the constrained problem of three magnetic vortices is a completely Liouville-integrable Hamiltonian system with two degrees of freedom. For this system, we find an augmented bifurcation diagram, perform a reduction to a system with one degree of freedom, and investigate level curves of the reduced Hamiltonian in detail. The obtained results show the presence of noncompact bifurcations and a noncritical bifurcation line. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider the periodic boundary value problem for two variants of a weakly dissipative complex Ginzburg–Landau equation. In the first case, we study a variant of such an equation that contains the cubic and quintic nonlinear terms. We study the problem of local bifurcations of traveling periodic waves under stability changes. We show that a countable set of two-dimensional invariant tori arises as a result of such bifurcations. Both types of bifurcations are possible in the considered formulation of the problem, soft (postcritical) and hard (subcritical) ones, depending on the choice of the coefficients in the equation. We obtain asymptotic formulas for the solutions forming the invariant tori. We also study the periodic boundary value problem for the equation that is called the nonlocal Ginzburg–Landau equation in physics. We show that the boundary value problem in the considered variant has an infinite-dimensional global attractor. We present the solutions forming such an attractor. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and Gödel metrics. We derive the Hamiltonian vector fields governing the system evolution, and construct and discuss the associated recursion operators generating the constants of motion. We also characterize relevant master symmetries. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Asymptotic analysis is used to study the existence, local uniqueness, and asymptotic stability in the sense of Lyapunov of a solution of a one-dimensional nonlinear system of reaction–diffusion equations with various types of quasimonotonicity of the functions describing reactions. A feature of the problem is the discontinuities (jumps) of these functions at a single point on the segment on which the problem is posed. The solution with a large gradient in the vicinity of the discontinuity point is studied. Sufficient conditions for the existence of a stable stationary solution of systems with various quasimonotonicity conditions are given. The asymptotic method of differential inequalities is used to prove the existence and stability theorems. The main distinctive features of this method for various types of quasimonotonicity are listed. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Results providing bounds of the nonwandering set of a mapping, hyperbolicity conditions, and the method of anti-integrability shed light on the global behavior of a discrete system. Following recent works, we use this approach to investigate the behavior of predator–prey systems in dimensions \(2\) and \(3\) . Our goal is not only to present results regarding the existence of Bernoulli shifts and hyperbolicity in the phase space but also to emphasize the applicability of this approach in a variety of interesting systems. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We consider an initial boundary value problem for a singularly perturbed parabolic system of two reaction–diffusion-type equations with Neumann conditions, where the diffusion coefficients are of different degrees of smallness and the right-hand sides need not be quasimonotonic. We obtain an asymptotic approximation of the stationary solution with a boundary layer and prove existence theorems, the asymptotic stability in the sense of Lyapunov, and the local uniqueness of such a solution. The obtained result is applied to a class of problems of chemical kinetics. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: We construct new substantive examples of nonautonomous vector fields on a \(3\) -dimensional sphere having simple dynamics but nontrivial topology. The construction is based on two ideas : the theory of diffeomorphisms with wild separatrix embedding and the construction of a nonautonomous suspension over a diffeomorphism. As a result, we obtain periodic, almost periodic, or even nonrecurrent vector fields that have a finite number of special integral curves possessing exponential dichotomy on \(\mathbb R\) such that among them there is one saddle integral curve (with a \((3,2)\) dichotomy type) with a wildly embedded \(2\) -dimensional unstable separatrix and a wildly embedded \(3\) -dimensional stable manifold. All other integral curves tend to these special integral curves as \(t\to \pm \infty\) . We also construct other vector fields having \(k\geqslant 2\) special saddle integral curves with the tamely embedded \(2\) -dimensional unstable separatrices forming mildly wild frames in the sense of Debrunner–Fox. In the case of periodic vector fields, the corresponding specific integral curves are periodic with the period of the vector field, and are almost periodic in the case of an almost periodic vector field. PubDate: 2022-07-01

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Moduli spaces of stable vector bundles and compactifications of these moduli spaces are closely related to Yang–Mills gauge field theory. This paper, along with the preprint [arXiv:2012.11194], is devoted to finding an appropriate compactification of the moduli space of stable vector bundles on an algebraic variety of dimension \(\geqslant 2\) . We consider admissible pairs \(((\widetilde S, \widetilde L), \widetilde E)\) , each of which consists of an \(N\) -dimensional admissible scheme \(\widetilde S\) of some class with a certain ample line bundle \(\widetilde L\) and of a vector bundle \(\widetilde E\) . An admissible pair can be obtained by a transformation (called a resolution) of a torsion-free coherent sheaf \(E\) on a nonsingular \(N\) -dimensional projective algebraic variety \(S\) to a vector bundle \(\widetilde E\) on a certain projective scheme \(\widetilde S\) . The notions of stability (semistability) for admissible pairs and of M-equivalence for admissible pairs in the multidimensional case are introduced. We also study relations of the stability (semistability) for admissible pairs to the classical stability (semistability) for coherent sheaves under the resolution and relations of the M-equivalence for semistable admissible pairs to the S-equivalence of coherent sheaves under the resolution. The obtained results are intended for constructing a compactification of the moduli space of stable vector bundles and an ambient moduli space of semistable admissible pairs. PubDate: 2022-07-01