0000000000067085
AUTHOR
T. Brugarino
Analytic solutions of the diffusion-deposition equation for fluids heavir than atmospheric air
A steady-state bi-dimensional turbulent diffusion equation was studied to find the concentration distribution of a pollutant near the ground. We have considered the air pollutant emitted from an elevated point source in the lower atmosphere in adiabatic conditions. The wind velocity and diffusion coefficient are given by power laws. We have found analytical solutions using or the Lie Group Analysis or the Method of Separation of Variables. The classical diffusion equation has been modified introducing the falling term with non-zero deposition velocity. Analytical solutions are essential to test numerical models for the great difficulty in validating with experiments.
Exact Solutions of the Two Dimensional Boussinesq and Dispersive Water Waves Equations
In this paper two-dimensional Boussinesq and dispersive water waves equations are investigated in exact solutions. The Exp-function method is used for seeking exact solutions of the equations through symbolic computation.
GROUP ANALYSIS AND SOME EXACT SOLUTIONS FOR THE THERMAL BOUNDARY LAYER
We perform the group analysis of the thermal boundary layer in laminar flow. We obtain the classification of the solutions in terms of the asymptotic velocity. Some solutions of the boundary layer equations, for some distributions of outer flow velocity, are obtained also.
Painlevé analysis and exact solutions for the coupled Burgers system
We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.
Some evolution equations arising in physics
In this paper we consider a new series of evolution equations generalizing the Korteweg-deVries (KdV) and Burgers equations, and we report recent advances on these equations together with the physical phenomena where they arise. In particular we consider a generalized Burgers' equation and we sketch a method for solution in series by using the theory of Sobolevskij and Tanabe. Then we study the KdV equation with nonuniformity terms and we describe various physical interpretation of this equation. We consider various particular cases in which varying solitonic solutions exist. Also we sketch a unicity theorem. Finally modified Burgers-KdV equations are considered.