Related papers: Nonlinear second order oscillators off resonance a…
In this paper we introduce some fully nonlinear second order operators defined as weighted partial sums of the eigenvalues of the Hessian matrix, arising in geometrical contexts, with the aim to extend maximum principles and removable…
We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
Non-linear effects on driven oscillations are important in many fields of physics, ranging from applied mechanics to optics. They are instrumental for quantum applications. A limitation is that the non-linearities known up to now are…
The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations.We show that the obtained oscillation criterion is a generalization of J. S.…
Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
Recently, it was observed that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In particular, under mild assumptions on the…
It is proven that second-order vectorial nonlinear differential systems y''=f(y) , possess a continuum of symmetric solutions. They are shown to possess a continuum of even solutions. If f(y) is an odd function of y , then y''=f(y) is shown…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
We construct even and odd nonlinear coherent states of a parametric oscillator and examine their nonclassical properties.It has been shown that these superpositions exhibit squeezing and photon antibunching which change with time.
Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
A second-order topological insulator in three dimensions refers to a topological insulator with gapless states localized on the hinges, which is a generalization of a traditional topological insulator with gapless states localized on the…
Under consideration are the construction and properties of some special class of second other tangent sets on using the technique of nonstandard analysis.
We consider an N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator with distinct frequencies of oscillation. The technique previously developed in [Acta Phys. Polon. B 36 (2005) 2115; Nucl. Phys. B 902 (2016) 95] is used to construct a…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
A Li\'enard type nonlinear oscillator of the form $\ddot{x}+kx\dot{x}+\frac{k^2}{9}x^3+\lambda_1 x=0$, which may also be considered as a generalized Emden type equation, is shown to possess unusual nonlinear dynamical properties. It is…