Symmetry reductions of systems of partial differential equations using conservation laws

There is a well established connection between one parameter Lie groups of transformations and conservation laws for differential equations. In this thesis, we construct conservation laws via the invariance and multiplier approach based on the wellknown result that the Euler-Lagrange operator annihilates total divergences. This technique will be applied to some plasma physics models. We show that the recently developed notion of the association between Lie point symmetry generators and conservation laws lead to double reductions of the underlying equation and ultimately to exact/invariant solutions for higher-order nonlinear partial di erential equations viz., some classes of Schr odinger and KdV equations.