84 citations · 738 across the 68 of their papers we have counts for
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On the variational noncommutative Poisson geometry
Arthemy V. Kiselev
We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)grad…
Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models
Arthemy V. Kiselev
We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in thre…
Gardner's deformations of the graded Korteweg-de Vries equations revisited
A. V. Kiselev, A. O. Krutov
We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this s…
A convenient criterion under which Z_2-graded operators are Hamiltonian
Veronique Hussin, Arthemy V. Kiselev
We formulate a simple and convenient criterion under which skew-adjoint Z_2-graded total differential operators are Hamiltonian, provided that their images are closed under commuta…