We firstly show how effective it is to utilize the invariant criteria for scalar linear (1+1) parabolic equations in order to perform reductions to the three Lie canonical forms of a bond-pricing model from finance. As a consequence we arrive at new results on bond-pricing equations that admit four nontrivial symmetries. In the second part we draw attention… (More)
The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.
When a circular jet of liquid strikes a sphere normal to the tangent plane at a point, a liquid film is formed on the surface of the sphere. This is a new problem. The flow in the liquid film is studied by means of boundary layer theory for laminar flow. The governing equations are Prandtl's momentum boundary layer equation and the continuity equation. To… (More)
—A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl's momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two… (More)