NONCLASSICAL POTENTIAL SYMMETRIES AND INVARIANT SOLUTIONS OF HEAT EQUATION

Some nonclassical potential symmetry generators and group-invariant solutions of heat equation and wave equation were determined. It is shown that some new explicit solutions of partial differential equations in conserved form can be constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot be obtained by using the Lie or Lie-B(a)cklund symmetry group generators of differential equations.