24 citations · 49 across the 18 of their papers we have counts for
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New 5th-order Schwarzian evolution equations and their higher-order symmetries
Marianna Euler, Norbert Euler
We report new quasilinear and fully-nonlinear 5th-order Schwarzian evolution equations. These are symmetry-integrable evolution equations in 1+1 dimensions, i.e. equations that adm…
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…
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…
On 2nd-order fully-nonlinear equations with links to 3rd-order fully-nonlinear equations
Marianna Euler, Norbert Euler
We derive the general conditions for fully-nonlinear symmetry-integrable second-order evolution equations and their first-order recursion operators. We then apply the established P…