Some Invariant Solutions for Unsaturated Flow Models with Plant Root Extraction

Abstract

Using two parameter symmetry groups we shall obtain exact
(invariant) solutions for a class of non-linear partial differential equations
which models soil water infiltration and redistribution in a bedded soil profile
irrigated by a drip irrigation system. Studying of such solutions is important
from the agricultural point of view because the solution will help to determine
the irrigation input while optimizing the production returns.
Mathematics Subject Classification (1991): 35Q35, 22S76
Keywords: plant root extraction, soil, water, infiltration, irrigation,
agricultural/other equations arising in fluid mechanics/symmetry, nonlinear,
partial differential equations, differential equations

Quaestiones Mathematicae
24(1) 2001, 9–19