Related papers: Reduction theorems for Noether's problem
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions…
In this paper, we prove the Noether theorem with the multiplicities described by PD operators. Despite the known analogue versions in this case the provided conditions are necessary and sufficient. We also prove the Cayley-Bacharach theorem…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
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.
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
We explain how to use Hoare's Theorem to find the signature of a subgroup of an NEC group. We give several examples.
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…
We find the Noether point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries are composed of a quasi-invariance transformation, a time-dependent rotation and a time-dependent spatial translation. The…
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…
Instantaneous derivation of the Thomas precession.
Noether theorem establishes an interesting connection between symmetries of the action integral and conservation laws of a dynamical system. The aim of the present work is to classify the damped harmonic oscillator problem with respect to…
In this article we use the Desargues' theorem and its reciprocal to solve two problems.
The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. $O$-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra,…
New reductions of the 2D Toda equations associated with low-triangular difference operators are proposed. Their explicit Hamiltonian description is obtained.