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This paper investigates the equivalence of parabolic partial differential equations to the
classical one‐dimensional heat equation using reciprocal transformations. The equations …

We introduce an integrable two-component extension of the general heavenly equation and
prove that the solutions of this extension are in one-to-one correspondence with 4 …

We develop a procedure to implement the method of quadric ansatz to a class of second
order partial differential equations (PDEs), which includes the four-dimensional Kähler …

We find the local form of all non-closed Lorentzian Weyl manifolds (M, c,∇) with recurrent
curvature tensor. The recurrent curvature tensor turns out to be weighted parallel, ie, the …

Recently, an infinitesimal approach for finding reciprocal transformations has been
proposed. The method uses the group analysis approach and consists of similar steps as for …