摘要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 ut=uxn+1+B(u)ux+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.
Abstract：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 ut=uxn+1+B(u)ux+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.
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