Related papers: Action-angle variables for the purely nonlinear os…
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving…
A central mechanism of linearised two dimensional shear instability can be described in terms of a nonlinear, action-at-a-distance, phase-locking resonance between two vorticity waves which propagate counter to their local mean flow as well…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $\phi_1$ and $\phi_2$ interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless…
Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We…
We investigate a generic non-phase invariant Hamiltonian model that governs the dynamics of nonlinear dispersive waves. We give evidence that initial data characterized by random phases naturally evolve into phase correlations between…
The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a successful approach. However, when the solution depends on elliptic functions the transformation to action-angle variables may need to remain in…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
Charged particle motion in axisymmetric toroidal magnetic fields is analyzed within the context of the canonical Hamiltonian Guiding Center theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic…
Analytical solution of the homoclinic orbit of a two dimensional system of differential equations that describes the hamiltonian part of the slow flow of a three degree of freedom dissipative system of linear coupled oscillators with an…
A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we…
A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and…
In this paper, He's frequency-amplitude formulation with some choice of location points that improve accuracy is applied to determine the periodic solution for the nonlinear oscillations of a punctual charge in the electric field of charged…
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…
We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the…