New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...

Animal treading can change soil physical properties, and thus is an important factor in hydrological modelling. We investigated the impacts of animal treading on infiltration by using a series of rainfall simulation experiments at Whatawhata Research Center, Waikato, New Zealand. The study identified significant variables for estimating soil steady-state infiltration at a microsite (0Ð5 m2) and...

In the present study, three-parameter one-dimensional vertical infiltration equation recently proposed by Poulovassilis and Argyrokastritis is examined. The includes saturated hydraulic conductivity (Ks), soil sorptivity (S), an additional parameter c; it valid for all times. c a fitting that depends on type of porous medium. characterized incorporation exact contribution pressure head gradient...

In this paper, we consider the generalised hierarchy of first Painlevé equation which is a sequence polynomial ordinary differential equations even order that have uniform differential-algebraic structure determined by operator L~n. The member for n = 2 equation, and subsequent 2n – contain arbitrary parameters. They are named as higher analogues order. article considers analytical properties s...