Reports on Mathematical Physics最新文献

We find an explicit solution formula of the time dependent self-dual equations of Chern—Simons—Higgs model. The solution is expressed completely in terms of initial data.

It is well known that the partition function of two-dimensional Ising model can be expressed as a Grassmann integral over the action bilinear in Grassmann variables. The key aspect of the proof of this equivalence is to show that all polygons, appearing in Grassmann integration, enter with fixed sign. For three-dimensional model, the partition function can also be expressed by Grassmann integral. However, the action resulting from low-temperature (L-T) expansion contains quartic terms, which do not allow explicit computation of the integral. We wanted to check — apparently not explored — the possibility that using the high-temperature (H-T) expansion would result in action with only bilinear terms (in two dimensions, L-T and H-T expansions are equivalent, but in three dimensions, they differ from each other). It turned out, however, that polygons obtained by Grassmann integration are not of fixed sign for any ordering of Grassmann variables on sites. This way, it is not possible to express the partition function of three-dimensional Ising model as a Grassmann integral over bilinear action.

In the present paper, it has been obtained that the fundamental group of n-dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for n = 2. Thereafter, it is extended to n > 2 by proving that loops nonhomotopic in M² continue to be nonhomotopic in Mⁿ using embedding of M² in Mⁿ as a retract through the projection map.

For a certain natural generalization of the Infeld—Rowlands equation we prove nonexistence of nontrivial local Hamiltonian structures and nontrivial local symplectic structures of any order, as well as of nontrivial local Noether and nontrivial local inverse Noether operators of any order, and exhaustively characterize all cases when the equation in question admits nontrivial local conservation laws of any order; the method of establishing the above nonexistence results can be readily applied to many other PDEs.

Based on Lie superalgebra sI(1, 2) and the TAH scheme, we derive (1+1)-dimensional and (2+1)-dimensional nonisospectral integrable hierarchies and the corresponding super Hamiltonian structures. At the same time, we construct a generalized Lie superalgebra sI(1, 2), and apply it to (1+1)-dimensional and (2+1)-dimensional integrable systems. Finally, we discuss the super Hamiltonian structures of (1+1)-dimensional and (2+1)-dimensional integrable hierarchies associated with Lie superalgebra$G$sI(1, 2).

In this paper, we construct a bi-covariant (h,h′)-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GL_h.h′ (1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields.

We consider an inverse problem for diffusion equation involving fractional Laplacian operator in space and Hilfer fractional derivatives in time with Dirichlet zero boundary conditions. The inverse problem is to recover time-dependent source term and diffusion concentration with an integral type over-determination condition. We discuss the analytical solution of the inverse problem and prove the existence and uniqueness of the analytical solution. Some special cases and examples for the considered inverse problem are provided.

A model of nonlinear elastic media containing cavities, microcracks, or soft inclusions is considered. We propose a modification of the well-known model to such media. The modification consists in taking into account those terms in the approximate equation of state that were discarded in the previously considered models. The main goal of the ongoing research is to show the persistence of the soliton-like solutions in the modified model, and to study their dynamical properties.

We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that the solution displays fractal behavior at irrational times, while exhibiting regularity similar to the initial data at rational times. These extend the results of Oskolkov [16] and Rodnianski [18] on the free Schrödinger evolution to the general case regarding potentials.