Theoretical and Mathematical Physics最新文献

We study the Schrödinger wave equation with an exponential potential in the context of a point-like global monopole. This exponential potential is composed of a generalized (q)-deformed Hulthen potential and a Yukawa-type potential. We incorporate the Greene–Aldrich approximation scheme to handle the centrifugal and other terms and obtain an approximate eigenvalue solutions in terms of special functions. We show that the eigenvalue solution is influenced by the topological defect with this exponential potential, and therefore breaks the degeneracy of the spectrum compared to the flat-space case. We then use this eigenvalue solution to analyze a few superposed potential models, and discuss the results.

We apply the gauge transformations (T_mathrm{D}) (differential type) and (T_mathrm{I}) (integral type) to study the discrete mKP hierarchies. We prove that (T_mathrm{D}) and (T_mathrm{I}) can be commutative and the product of (T_mathrm{D}) and (T_mathrm{I}) satisfies the Sato equation. By means of gauge transformations, we arrive at the necessary and sufficient condition for reducing the generalized Wronskian solutions to constrained hierarchies. Finally, we give an example in the Appendix.

We investigate the standard binary Darboux transformation (SBDT) for an (M)-component sdC integrable system. For this, we construct the Darboux matrix using specific eigenvector solutions associated to the Lax pair, not only in the direct space but also in the adjoint space, resulting in the binary Darboux matrix. By the iterative application of the SBDT, we derive quasi-Grammian soliton solutions of the (M)-component sdC integrable system. We also examine the Darboux transformation (DT) applied to matrix solutions of the sdC integrable system, expressing solutions using quasideterminants. Additionally, we thoroughly discuss the DT applied to scalar solutions of the system, expressing solutions as ratios of determinants. Furthermore, we investigate the SBDT and its application to obtaining quasi-Grammian multikink and multisoliton solutions for the (M)-component sdC integrable system. Additionally, we demonstrate that quasi-Grammian solutions can be simplified to elementary solutions by reducing spectral parameters.

A non-self-adjoint fourth-order differential operator with nonsmooth coefficients and periodic boundary conditions is considered. Results concerning the asymptotics of the spectrum of this operator are obtained.

The Cauchy matrix approach is developed for solving nonisospectral Kadomtsev–Petviashvili equation and the nonisospectral modified Kadomtsev–Petviashvili equation. By means of a Sylvester equation ( boldsymbol{L} boldsymbol{M} - boldsymbol{M} boldsymbol{K} = boldsymbol{r} boldsymbol{s} ^{mathrm T}), a set of scalar master functions ({S^{(i,j)}}) are defined. We derive the evolution of scalar functions using the nonisospectral dispersion relations. Some explicit solutions are illustrated together with the analysis of their dynamics.

We find universal characteristic identities for the (3)-split Casimir operator in the representation (operatorname{ad}^{otimes 3}) of the (osp(M|N)) and (sl(M|N)) Lie superalgebras. Using these identities, we construct projectors onto the invariant subspaces of these representations and find universal formulas for their superdimensions. All the formulas are in accordance with the universal description of subrepresentations of the (operatorname{ad}^{otimes 3}) representation of simple basic Lie superalgebras in terms of the Vogel parameters.

We use a recently proposed scheme of matrix extension of dispersionless integrable systems in the Abelian case, leading to linear equations related to the original dispersionless system. In the examples considered, these equations can be interpreted in terms of Abelian gauge fields on the geometric background defined by a dispersionless system. They are also connected with the linearization of the original systems. We construct solutions of these linear equations in terms of wave functions of the Lax pair for the dispersionless system, which is represented in terms of some vector fields.

We construct a nonstandard Lagrangian, called the multiplicative form, for a homogeneous scalar field and a fermion field via the inverse calculus of variations with the equations of motion that still satisfy the respective Klein–Gordon and Dirac equations. By employing the nonuniqueness of the Lagrangian, we show that the Lagrangians can be written as linear combinations of the standard and nonstandard Lagrangians. The stability of the ghost field, an unnatural smallness of the cosmological constant, and the chiral condensate are discussed by using these new Lagrangians.

We continue studying the phenomenological model in which dark energy in the form of the cosmological constant is identified with the mean of the energy–momentum tensor of the causally disconnected region. We completely define the time-dependent model parameter and clarify its physical meaning. We find the scalar field potential corresponding to the proposed approach. We show that two stages of superfast expansion of the Universe existed. The the Universe heating stage occurred naturally due to the positive definiteness requirement for the energy and is reflected in the obtained scalar field potential.

The self-gravitating Higgs field of a scalar charge is studied in the case of an asymmetric scalar doublet containing not only the canonical but also a phantom component. We show that in the zeroth and first approximation in the smallness of the canonical and phantom scalar charges, the gravitational field of the scalar charge is described by the Schwarzschild–de Sitter metric with a cosmological constant determined by a stable equilibrium point — the vacuum potential of the canonical Higgs field and the zero value of the scalar potential. An equation for the perturbation of the stable value of the potential is obtained and studied, and the asymptotic behavior in the near and far zones is found. The averaging of microscopic oscillations of the scalar field is carried out and it is shown that the sign of the contribution of microscopic oscillations to the macroscopic energy of the scalar field is completely determined by the values of the fundamental constants of the Higgs potential of the asymmetric scalar doublet. Particular attention is paid to the case where the contribution of oscillations to the macroscopic energy and pressure densities is strictly equal to zero. Possible applications of the obtained solutions are discussed.