摘要
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 he constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot he obtained by using the Lie or Lie-Baeicklund symmetry group generators of differential equations.
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 he constructed by using the nonclassical potential symmetry generators which are derived from their adjoint system. These explicit solutions cannot he obtained by using the Lie or Lie-Baeicklund symmetry group generators of differential equations.
基金
Project supported by the National Natural Sciences Foundation of China (No.10272021) and the Doctoral Program Foundation of Education Ministry of China (No.20040007022)
