Russian Journal of Mathematical Physics最新文献

We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given.

We study a discrete Miura-type transformation between the hierarcies of non-Abelian semi-infinite Volterra (Kac–van Moerbeke) and Toda lattices with operator coefficients in terms of the inverse spectral problem for three-diagonal band operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl operator-valued function, can be used in solving initial-boundary value problem for the systems of both these hierarchies. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra hierarchy and the Toda sub-hierarchy which can be characterized via Lax operators corresponding to its lattices.

An algorithmic concept of the physical world is proposed in which the main ideas of the Darwinian evolution act as algorithms of becoming.

We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real and complex resonances.

An analogue of reflexivity in asymmetric cone spaces is introduced and studied. Some classical results known for ordinary normalized spaces are carried over to the case of essentially asymmetric spaces.

It is known that the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra. The aim of this paper is to consider the (lambda)-shift algebra, which is a (lambda)-analogue of the shift algebra, and to study (lambda)-analogues of Whitney numbers of the first kind (called (lambda)-Whitney numbers of the first kind) and those of (r)-Whitney numbers of the first kind arising from normal orderings in the (lambda)-shift algebra. From the normal orderings in the (lambda)-shift algebra, we derive some explicit expressions and recurrence relations on both of those numbers.

We prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and connected, which is known, but also commutative.

Recently we have shown that the equivalence classes of metrics on the double of a metric space (X) form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of (X), which is more computable. As a special case, we study this subsemigroup related to the family of geodesic rays starting from the basepoint, for Euclidean spaces and for trees.

Properties of local solarity and regularity in essentially asymmetric locally uniformly rotund spaces are studied. The results obtained are applied to the study of smooth solutions of the eikonal equation (|nabla u|equiv 1). For this purpose, sets of regular points are investigated. Examples of the influence of caustics on the evolution of elliptical galaxies into spiral ones are given.

We consider a generalization of the mKdV equation which contains dissipation terms similar to those contained in both the Benjamin–Bona–Mahoney equation and the famous Camassa–Holm and Degasperis–Procesi equations. Our objective is the construction of classical (solitons) and non-classical (peakons and cuspons) solitary wave solutions of this equation.