We show that iterations of the nonclassical symmetries method for any evolution equation give raise to new nonlinear equations, which inherit the symmetry algebra of the given equation. Invariant solutions of these heir-equations supply new solutions of the original equation. The same method generates heir-equations for hyperbolic and elliptic equations. Some examples are given.
NUCCI, M.C. (1994). Iterating the nonclassical symmetries method. PHYSICA D-NONLINEAR PHENOMENA, 78(1-2), 124-134 [10.1016/0167-2789(94)00125-1].
Iterating the nonclassical symmetries method
NUCCI, Maria Clara
1994
Abstract
We show that iterations of the nonclassical symmetries method for any evolution equation give raise to new nonlinear equations, which inherit the symmetry algebra of the given equation. Invariant solutions of these heir-equations supply new solutions of the original equation. The same method generates heir-equations for hyperbolic and elliptic equations. Some examples are given.File in questo prodotto:
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