Related papers: A symmetry reduction technique for higher order Pa…
In this paper, we discuss a general approach to find periodic solutions bifurcating from equilibrium points of classical Vlasov systems. The main access to the problem is chosen through the Hamiltonian representation of any Vlasov system,…
We consider the 3D Mikhalev system, $$ u_t=w_x, \quad u_y= w_t-u w_x+w u_x, $$ which has first appeared in the context of KdV-type hierarchies. Under the reduction $w=f(u)$, one obtains a pair of commuting first-order equations, $$…
We approach the construction of Backlund transformations for Darboux integrable hyperbolic partial differential equations in the plane through the reduction of exterior differential systems. For example it is shown that all the Backlund…
In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…
The conserved densities of hydrodynamic type system in Riemann invariants satisfy a system of linear second order partial differential equations. For linear systems of this type Darboux introduced Laplace transformations, generalising the…
Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such…
This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the ''podmodeli'' (submodels) program outlined by Ovsyannikov (1994). We consider the case of the special state equation, prescribing pressure…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive.
The goal of this article is to prove that the determinantal formulas of the Painlev'e 2 system identify with the correlation functions computed from the topological recursion on their spectral curve for an arbitrary non-zero monodromy…
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is…
In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…
In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems,…
An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be…
We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…
Dirac brackets are widely used to study constrained Hamiltonian dynamics. In this paper we develop a Dirac-bracket approach to normal forms on momentum levels and relate it to symplectic reduction in the cases where reduction yields a…
Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for…
A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas law is shown to admit an integrable elliptic vortex reduction when $\gamma=2$ to a nonlinear dynamical subsystem with underlying integrable Hamiltonian-Ermakov…
This work presents a geometric formulation for transforming nonconservative mechanical Hamiltonian systems and introduces a new method for regularizing and linearizing central force dynamics -- in particular, Kepler and Manev dynamics --…
The multi-symplectic form for Hamiltonian PDEs leads to a general framework for geometric numerical schemes that preserve a discrete version of the conservation of symplecticity. The cases for systems or PDEs with dissipation terms has…