We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.

An exact solution of a two dimensional RSOS model of wetting at a corrugated (periodic) wall is found using transfer matrix techniques. In contrast to mean-field analysis of the same problem the wetting transition remains second-order and occurs at a lower temperature than that of the planar system. Comparison with numerical studies and other analytical approaches is made.

We illustrate the description of correlated subsystems by studying the simple two-body Hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in the framework of the density matrix formalism, describes correlations in the electron-proton motion.

Agglomeration processes in non-interacting particle systems can be understood from a thermodynamic point of view. If the enthalpy of agglomeration is negligible, the distribution of agglomeration states adopts the state of highest entropy. Herein, we provide the exact analytical solution to the mole fractions of agglomerates comprising i monomers, xi =2-i .

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic...

In this paper we study 1D k-neighbor Ising model. Variational approach using modified nearestneighbor interaction strength is developed, but the optimization of the coupling constant appears at least as hard as the exact solution in the general case. For the exact solution two formulations of transfer matrix are studied: the block-spin approach yielding matrix T and the ’sliding window’ approac...

To formulate a single-leg seat inventory control problem in an airline ticket sales system, the concept and techniques of revenue management are applied in this research. In this model, it is assumed the cabin capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two groups of early-reserving and late-purchasing customers demanding t...