Related papers: Contact Integrable Extensions and Zero-Curvature R…
A procedure is described to associate fibre bundles over the circle to two- dimensional theories with defects which have their field equations and defects described by a zero curvature condition.
We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE)…
We show that Pleba\'nski's equation for self-dual metrics is equivalent to a pair of equations describing canonical transformations in 2-dimensional phase spaces. Examples of linearizations of these equations are given.
It is shown that the space of null geodesics of a star-shaped causally simple subset of Minkowski space is contactomorphic to the canonical contact structure in the spherical cotangent bundle of $\mathbb{R}^n$. In the $3$-dimensional case…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
We apply Cartan's method of equivalence to find a contact integrable extension for the structure equations of the symmetry pseudo-group of the four-dimensional Martinez Alonso - Shabat equation. From the extension we derive two differential…
We give a simple prescription for relating different solutions to the zero-rest-mass field equations in conformally flat space-time via complex conformal transformations and changes in reality conditions. We give several examples including…
The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the…
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
Backlund transformations are used to search for solutions, particularly soliton solutions, of non-linear differential equations. In this paper we present an invariant geometrical theory of Backlund transformations for second order evolution…
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the pseudogroup of contact transformations.…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
There are investigated the Lie algebraic structure and integrability properties of a very interesting class of nonlinear dynamical systems called the heavenly equations, which were initiated by Pleba\'nski and later analyzed in a series of…
The exact and approximate solutions of singular integro-differential equations relating to the problems of interaction of an elastic thin finite or infinite non-homogeneous patch with a plate are considered, provided that the materials of…
We introduce a notion of the noncommutative integrability within a framework of contact geometry.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of…
We provide a higher dimensional extension of the gravitational decoupling method. This extended method allows to obtain new analytic and well behaved solutions that could be associated to higher dimensional stellar distributions.…
A very simple method is devised to derive a (strictly) isospectral extension of the Morse potential. Furthermore, point canonical transformations are used to transform the latter into quasi-exactly solvable extensions of the radial…
Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…