Conditional Lie Backlund Symmetries of Hamilton--Jacobi Equations

symmetry method, as a generalization of the conditional symmetry and Lie Backlund symmetry methods, is developed to study the Hamilton--Jacobi equations. It is shown that the equation u_t=u_xⁿ⁺¹+B(u)u_x+C(u) admits a class of conditional Lie Backlund symmetry for certain functions B(u) and C(u). As a result, a complete description of structure of solutions to the resulting equations associated to the conditional Lie Backlund symmetry is performed.