On differential equations invariant under a projective transformation group
On differential equations invariant under a projective transformation group
We consider a projective transformation and establish the invariants for this transformation group up to order seven. We use the obtained invariants to construct a class of nonlinear evolution equations and identify some symmetry-integrable equations in this class. Notably, the only symmetry-integrable evolution equation of order three in this class is a fully-nonlinear equation for which we find the recursion operator and its connection to the Schwarzian KdV. We furthermore establish that higher-order symmetry-integrable equations in this class belong to the hierarchy of the fully-nonlinear 3rd-order equation and prove this for the 5th-order case. We also identify the ordinary differential equations that are invariant under this projective transformation and reduce the order of these equations.
Norbert Euler、Marianna Euler
数学
Norbert Euler,Marianna Euler.On differential equations invariant under a projective transformation group[EB/OL].(2025-05-14)[2025-07-23].https://arxiv.org/abs/2505.09800.点此复制
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