Related papers: A simple frequency approximation formula for a cla…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
Since years a classical oscillator is known representing fundamental properties of quantum mechanical systems without the use of the demanding mathematics of quantum theory. This allows to develop an intuitive notion in introductory quantum…
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Solutions of nonlinear acoustic equations describing propagation of strong sound pulses with account of curvature of wave fronts in multi-dimensional geometry are obtained from simple physical considerations. The form of these solutions…
We present an elementary approach to observe frequency cascade on forced nonlinear Schr{\"o}dinger equations. The forcing term (which may also appear as a potential term instead) consists of a constant term, perturbed by a modulated…
We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the…
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
A new method for examining the possible space-time variation of the fine structure constant ($\alpha$) is proposed. The technique uses a relatively simple measurement with an optical resonator to compare atom-stabilized optical frequency…
We consider frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. An important type of such resonators are nano- and micro-electro-mechanical systems. Various noise sources are considered, with the…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
In many industrial applications, signals with short periodic pulses, caused by repeated steps in the manufacturing process, are present, and their fundamental frequency or period may be of interest. Fundamental frequency estimation is in…
We demonstrate an analytical method for calculating the phase sensitivity of a class of oscillators whose phase does not affect the time evolution of the other dynamic variables. We show that such oscillators possess the possibility for…
We present a method for constructing superoscillatory functions the superoscillatory part of which approximates a given polynomial with arbitrarily small error in a fixed interval. These functions are obtained as the product of the…
We estimate simple combination of the parabolic cylinder functions and their derivatives. These estimates are important for the spectral analysis of non-analytically perturbed quantum harmonic oscillator. The estimates are valid in rather…