The magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent is studied. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables b...

The aim of this paper is to develop a model of the respiratory system. The real bronchial tree is embedded within the parenchyma, and ventilation is caused by negative pressures at the alveolar level. We aim to describe the series of pressures at alveolae in the form of a function, and to establish a sound mathematical framework for the instantaneous ventilation process. To that end, we treat t...

The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are introduced to reduce theories on an infinite lattice to those on semi-infinite, or finite ones.