Related papers: Generating a chain of maps which preserve the same…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…
We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential…
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…
We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables…
The Kaczmarz algorithm is an iterative method for solving a system of linear equations. It can be extended so as to reconstruct a vector $x$ in a (separable) Hilbert space from the inner-products $\{\langle x, \phi_{n} \rangle\}$. The…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic…
The method of obtaining new integrable coupled equations through enlarging spectral problems of known integrable equations, which was recently proposed by W.-X. Ma, can produce nonintegrable systems as well. This phenomenon is demonstrated…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
Various new two-component systems related to the lattice Schwarzian Boussinesq equation are constructed in a systematic way from conservation laws. Their multidimensional consistency is demonstrated, Lax pairs, symmetries and conservation…
Symmetry reductions of systems of two nonlinear partial differential equations are studied. We find ansatzes reducing system of partial differential equations to system of ordinary differential equations. The method is applied to system…
In this paper we consider generalization of procedure of construction of potential systems for systems of partial differential equations with multidimensional spaces of conservation laws. More precisely, for construction of potential…
Generalized Darboux-Halphen (gDH) systems, which form a versatile class of three-dimensional homogeneous quadratic differential systems (HQDS's), are introduced. They generalize the Darboux-Halphen (DH) systems considered by other authors,…
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite…
The structure-preserving doubling algorithm (SDA) is a fairly efficient method for solving problems closely related to Hamiltonian (or Hamiltonian-like) matrices, such as computing the required solutions to algebraic Riccati equations.…
Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a new method to generate new integrable systems through making perturbation in matrix spectral problems for integrable couplings, which is…
It is shown, how to generate infinite sequences of differential equations of the second order based on some standard equations, using Euler-Imshenetsky-Darboux (EID) transformation. For all this, factorizations of differential operators and…
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial…