Heir-equations were found by iterating the nonclassical symmetry method. Apart inheriting the same Lie symmetry algebra of the original partial differential equation, and thus yielding more (and different) symmetry solutions than expected, the heir-equations are connected to conditional Lie-Baecklund symmetries, and generalized conditional symmetries; moreover they solve the inverse problem, namely a special solution corresponds to the nonclassical symmetry. A review of 25-year work is presented, and open problems are brought forward.
Heir-equations for partial differential equations: a 25-year review / M. C. Nucci. - STAMPA. - 2:(2020), pp. 188-205.
Heir-equations for partial differential equations: a 25-year review
M. C. Nucci
2020
Abstract
Heir-equations were found by iterating the nonclassical symmetry method. Apart inheriting the same Lie symmetry algebra of the original partial differential equation, and thus yielding more (and different) symmetry solutions than expected, the heir-equations are connected to conditional Lie-Baecklund symmetries, and generalized conditional symmetries; moreover they solve the inverse problem, namely a special solution corresponds to the nonclassical symmetry. A review of 25-year work is presented, and open problems are brought forward.| File | Dimensione | Formato | |
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