On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional

A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.

Soliton structures in optical fiber communications with Kundu–Mukherjee–Naskar model

In the present work, we investigate soliton structures in optical fiber communications. The medium is described by the Kundu–Mukherjee–Naskar model. With the aid of the ansatz approach, the exact solutions are constructed. Consequently, distinct wave structures including W-shaped, bright and dark solitons are derived. These new soliton solutions are retrieved under certain parametric conditions. Besides, it is found that the bright soliton has two different types in a particular limit. Optical solitons are displayed graphically to shed light on their behaviors.

A New Model for Calculating the Ground and Excited States Masses Spectra of Doubly Heavy Ξ Baryons

Since the doubly heavy baryons masses are experimentally unknown (except Ξcc+ and Ξcc++), we present the ground state masses and the positive and negative parity excited state masses of doubly heavy Ξ baryons. For this purpose, we have solved the six-dimensional hyperradial Schrödinger equation analytically for three particles under the hypercentral potential by using the ansatz approach. In this paper, the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term, and tensor term) to the hypercentral potential. Our obtained masses for the radial excited states and orbital excited states of Ξccd, Ξccu, Ξbbd, Ξbbu, Ξbcd, and Ξbcu systems are compared with other theoretical reports, which could be a beneficial tool for the interpretation of experimentally unknown doubly heavy baryons spectrum.

Optical Solitons in Magneto-optic Waveguides with Spatio-temporal Dispersion

This paper obtains the exact solution for solitons propagating through magneto-optic waveguides. There are three forms of nonlinear media that are considered. They are Kerr law, power law and log-law nonlinearity. The ansatz approach retrieves bright, dark as well as singular soliton solutions. There are several constraint conditions that needs to be in place for the solitons and Gaussons to exist.