Related papers: Symmetry, Hamiltonian Problems and Wavelets in Acc…

A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…

This paper aims to show that there exist non-symmetry constraints which yield integrable Hamiltonian systems through nonlinearization of spectral problems of soliton systems, like symmetry constraints. Taking the AKNS spectral problem as an…

Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high…

Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…

In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.

We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of…

In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…

In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…

The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses…

Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this…

A new approach to the solution of quasilinear nonelliptic first-order systems of inhomogeneous PDEs in many dimensions is presented. It is based on a version of the conditional symmetry and Riemann invariant methods. We discuss in detail…

The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of…

We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…

Any given system of ordinary differential equations in $n$-dimensional configuration space can be obtained from a peculiar variational problem with one local symmetry. The obtained action functional leads to the Hamiltonian formulation in…

A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region. Therefore, most methods are based on a truncation technique and the computational cost is then very high if…