Related papers: Completely Integrable Replicator Dynamics Associat…
We review our work on the relation between integrability and infinite-dimensional algebras. We first consider the question of what sets of commuting charges can be constructed from the current of a \mbox{\sf U}(1) Kac-Moody algebra. It…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model,…
In the article at hand, we sketch how, by utilizing nilpotency to its fullest extent (Engel, Super Engel) while using methods from the theory of universal enveloping algebras, a complete description of the indecomposable representations may…
We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and…
Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $\nu$, of the eigenfunctions are considered. The billiards for which the time-independent Schr\"odinger equation (Helmholtz equation) is…
We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend…
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an…
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…
The complete integrability of the Ostrovsky-Vakhnenko equation is studied by means of symplectic gradient-holonomic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related…
We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over the…
This paper extends the semiconservative quasispecies equations to account for arbitrary post-replication lesion repair efficiency. Such an extension could be an important tool for understanding processes such as cancer development and stem…
A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants. Exact solutions described by these…
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
We present an L-A pair for the Apel'rot case of a heavy rigid 3-dimensional body. Using it we give an algebro-geometric integration procedure. Generalizing this L-A pair, we obtain a new completely integrable case of the Euler-Poisson…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
This study uses the Lotka Volterra Predator-Prey model to offer a notion of piecewise patterns for the various piecewise derivatives. Using the piecewise derivatives, we produced numerical solutions that are referred to as the…
The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the…
We introduce and develop a class of \textit{Cantor-winning} sets that share the same amenable properties as the classical winning sets associated to Schmidt's $(\alpha,\beta)$-game: these include maximal Hausdorff dimension, invariance…
The theory of triples of Poisson brackets and related integrable systems, based on a classical R-matrix R in End_F(g), where g is a finite dimensional associative algebra over a field F viewed as a Lie algebra, was developed by…