Related papers: Some new integrable systems of two-component fifth…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…
Recently one integrable model with a cubic first integral of motion has been studied by Valent using some special coordinate system. We describe the bi-Hamiltonian structures and variables of separation for this system.
Exploiting the residual gauge freedom in the formulation of constrained KP hierarchy a number of new integrable systems are derived including hierarchies of Kundu-Eckhaus equation and higher order nonlinear extensions of Yajima-Oikawa and…
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. These…
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this paper new $1$-rotational 2-Steiner systems for different admissible $v,k$ pairs are introduced. In particular, $1$-rotational unitals of order $4$ are enumerated.
The linked systems of symmetric group divisible designs of type II is introduced, and several examples are obtained from affine resolvable designs and mutually UFS Latin squares. Furthermore, an equivalence between such symmetric group…
Some aspects of multidimensional soliton geometry are considered.
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. In particular, the family includes the so called contact oscillator, which has been used as a test…
We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We…
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…
Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…
All exactly integrable systems connected with the semisimple algebras of the second rank with an arbitrary choice of the grading in them are presented in explicit form. General solution of such systems are expressed in terms of the matrix…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
The recursion operator and bi-Hamiltonian formulation of the Drinfeld- Sokolov system are given
We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial…
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake…
We review recent developments of soliton theories and integrable systems on noncommutative spaces. The former part is a brief review of noncommutative gauge theories focusing on ADHM construction of noncommutative instantons. The latter…