Related papers: On a simple approach to nonlinear oscillators
The reality of neutrino oscillations has not really sunk in yet. The phenomenon presents us with purely quantum mechanical effects over macroscopic time and distance scales (milliseconds and 1000s of km). In order to help with the…
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…
We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.
This paper applies He's new amplitude-frequency relationship recently established by Ji-Huan He (Int J Appl Comput Math 3 1557-1560, 2017) to study periodic solutions of strongly nonlinear systems with odd nonlinearities. Some examples are…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
Singular exponential nonlinearities of the form $e^{h(x)\epsilon^{-1}}$ with $\epsilon>0$ small occur in many different applications. These terms have essential singularities for $\epsilon=0$ leading to very different behaviour depending on…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
In the present article, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear…
A completely analytical theory of chirped-pulse oscillators is presented. The theory is based on an approximate integration of the generalized nonlinear complex Ginzburg-Landau equation. The obtained parametric space of a chirped-pulse…
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
It is shown that the derivation of standard oscillation phase in the plane wave approximation without equal energy assumption is fraught with inconsistencies.
The frenetic growth of the need for computation performance and efficiency, along with the intrinsic limitations of the current main solutions, is pushing the scientific community towards unconventional, and sometimes even exotic,…
The calculation presented in "A neoclassical calculation of rotation profiles and comparison with DIII-D measurements" by Stacey, Johnson, and Mandrekas, [Physics of Plasmas, 13, (2006)], contains several errors, including the neglect of…
In this report, we lay the foundation for amplitude noise and phase noise analysis in nonlinear devices. We build a theoretical framework that helps us to analyze extremely difficult problems which include both nonlinearity and noise of…
We propose in this paper to study the solutions of some nonlinear elliptic equations with singular potential.
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…
Symplectic tomographies of classical and quantum states are shortly reviewed. The concept of nonlinear f-oscillators and their properties are recalled. The tomographic probability representations of oscillator coherent states and the…
We present several ideas in direction of physical interpretation of $q$- and $f$-oscillators as a nonlinear oscillators. First we show that an arbitrary one dimensional integrable system in action-angle variables can be naturally…
Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they…