4 papers
On differential equations invariant under a projective transformation group: integrability and reductions
Marianna Euler, Norbert Euler, Francesco Oliveri
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 nonline…
Two sequences of fully-nonlinear evolution equations and their symmetry properties
Marianna Euler, Norbert Euler
We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highes…
From fully-nonlinear to semilinear evolution equations: two symmetry-integrable examples
Marianna Euler, Norbert Euler
In this paper we derive two examples of fully-nonlinear symmetry-integrable evolution equations with algebraic nonlinearities, namely one class of 3rd-order equations and a 5th-ord…
Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
Marianna Euler, Norbert Euler
The term multipotentialisation of evolution equations in dimensions refers to the process of potentialising a given evolution equation, followed by at least one further poten…