We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae fo...

The optimization of technical processes requires a sufficient understanding of the interrelations in a process. More specifically, this means that a model of the given process is needed. Traditional methods for modeling technical processes are based on analytical relationships that are either explicit formulas derived from knowledge in physics, chemistry or engineering science or given as solut...

In this paper the problem of the theory of a quasicrystal structures-the determination of coordinates of each atom of quasicrystal in analytical form-is solved. Within the framework of the proposed model a periodic crystal can be presented as a particular case of a quasicrystal. The simple and explicit analytical formulas which describe the location of each atom in a quasicrystal are given. The...

In this paper the problem of the theory of a quasicrystal structures-the determination of coordinates of each atom of quasicrystal in analytical form-is solved. Within the framework of the proposed model a periodic crystal can be presented as a particular case of a quasicrystal. The simple and explicit analytical formulas which describe the location of each atom in a quasicrystal are given. The...

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been der...

We suggest a method for integrating sub-families of a family of nonlinear Schrödinger equations proposed by H.-D. Doebner and G.A. Goldin in the 1+1 dimensional case which have exceptional Lie symmetries. Since the method of integration involves non-local transformations of dependent and independent variables, general solutions obtained include implicitly determined functions. By properly speci...

We present a fundamental solution to an initial value problem for the KdV-Whitham system in an explicit integral form. Monotonically decreasing initial data with finite number of breaking points are considered. Generating function for the commuting flows of the averaged KdV hieararchy producing the analytical solutions to the KdV-Whitham system is constructed.

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...