Differential geometric prolongations of solution equations

This thesis is a study in the field of partial differential equations on differentiable manifolds. In particular non-linear evolution equations with solution solutions are studied by means of differential geometric tools and methods. Differential geometric prolongation technique is applied to the A.K.N.S. system as a unifying system for known 2-dimension solutions. Solution properties are studied in this differential geometric set up. The results are used to obtain a possible model for n-dimensional solutions.