Evidently, the linear superposition principle can not be exactly established as a general
principle in the presence of nonlinearity, and, at the first glance, there is no expectation for it …

Abstract We consider (3+ 1)-dimensional second-order evolutionary PDEs where the
unknown u enters only in the form of the 2nd-order partial derivatives. For such equations …

Einstein–Weyl geometry is a triple (D, g, ω) where D is a symmetric connection,[g] is a
conformal structure and ω is a covector such that∙ connection D preserves the conformal …

We study second-order partial differential equations (PDEs) in four dimensions for which the
conformal structure defined by the characteristic variety of the equation is half-flat (self-dual …

Equations of dispersionless Hirota type F (u_ x_ix_j)= 0 F (uxixj)= 0 have been thoroughly
investigated in mathematical physics and differential geometry. It is known that the …

We develop a method for describing invariant Monge-Amp\ere equations in the sense of V.
Lychagin and T. Morimoto (MAE) on a homogeneous contact manifold $ N $ of a semisimple …

This paper contains a thorough introduction to the basic geometric properties of the manifold
of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian …

In this work, we investigate a symmetry reduction of the recently discovered (3+ 1)-
dimensional equation of the Monge-Ampère type. This equation forms a bi-Hamiltonian …

We show that evolutionary Hirota type Euler-Lagrange equations in $(2+ 1) $ dimensions
have a symplectic Monge-Ampère form. We consider integrable equations of this type in the …

In this letter I analyze a covering jet manifold scheme, its relation to the invariant theory of
the associated vector fields, and applications to the Lax-Sato-type integrability of nonlinear …