Conditional Lie Bäcklund symmetries of Hamilton–Jacobi equations

The conditional Lie Bäcklund symmetry method, as a generalization of the conditional symmetry and Lie Bäcklund symmetry methods, is developed to study Hamilton–Jacobi equations. It is shown that two Hamilton–Jacobi equations admit conditional Lie Bäcklund symmetries of second-order for certain smooth functions. As a result, a complete description of the structure of solutions to the resulting equations associated with the conditional Lie Bäcklund symmetries is performed.