Related papers: Pseudo-orthogonal groups and integrable dynamical …
It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…
Various algebraic structures of degenerate four-wave mixing equations of optical phase conjugation are analyzed. Two approaches (the spinorial and the Lax-pair based), complementary to each other, are utilized for a systematic derivation of…
We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
To capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. These models are able to capture in a simple and compact way the complex behaviour of…
We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of…
In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This…
A method for determining the dimension and state space geometry of inertial manifolds of dissipative extended dynamical systems is presented. It works by projecting vector differences between reference states and recurrent states onto local…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group…
The present paper explores substitution minimal systems and their relation to stationary Bratteli diagrams and stationary dimension groups. The constructions involved are algorithmic and explicit, and render an effective method to compute…
We review some recent results on how PT-symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the…
This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus,…