Related papers: Non-integrability of the generalised spring-pendul…
In this paper we study the integrability of the Hamiltonian system associated to the fourth Painlev\'{e} equation. We prove that one two parametric family of this Hamiltonian system is not integrable in the sense of the Liouville-Arnold…
The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example a hard-disks is offered. This approach was based on Hamilton and Liouville generalized…
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the…
In this study, we consider a spring-block system that approximates a $d$-dimensional linear elastic body, where $d=2$ or $d=3$. We derive a $d\times d$ matrix as the spring constant using the P1 finite element method with a triangular mesh…
We say a $d$-dimensional simplicial complex embeds into double dimension if it embeds into the Euclidean space of dimension $2d$. For instance, a graph is planar iff it embeds into double dimension. We study the conditions under which the…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…
This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
We study a class of symmetric critical points in a variational $2D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3\times 3$ matrices. These critical points play the role of…
Let $K/\mathbf{Q}_p$ be an unramified extension of degree $f$ with residue field $k$. Let $\sigma$ be an irreducible representation of $\mathrm{GL}_n(k)$ over $\overline{\mathbf{F}}_p$. For $n\ge 3$, we prove that the universal…
In this work we consider the Hide-Skeldon-Acheson dynamo model \[ \dot x=x(y-1)-\beta z, \quad \dot y =\alpha(1-x^2)-\kappa y, \quad \dot z =x-\lambda z, \] where $\alpha,\beta,\kappa$ and $\lambda$ are parameters. We contribute to the…
We develop an effective two-dimensional coarse-grained description for the coupled system of a planar fluid membrane anchored to a thin layer of polar ordered active fluid below. The macroscopic orientation of the active fluid layer is…
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks…
In this work we use a recently developed nonintegrability theorem of Morales and Ramis to prove that the Friedmann Robertson Walker cosmological model with a conformally coupled massive scalar field is nonintegrable.
Two-dimensional reductions of the KP-Whitham system, namely the overdetermined Whitham modulation system for five dependent variables that describe the periodic solutions of the Kadomtsev-Petviashvili equation, are studied and…
We argue the integrability of the generalized KdV(GKdV) equation using the Painlev\'e test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlev\'e test but does not for $d \geq 3$ dimensional space. We also apply the…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
This paper studies the dynamics and integrability of a variable-length coupled pendulum system. The complexity of the model is presented by joining various numerical methods, such as the Poincar\'e cross-sections, phase-parametric diagrams,…