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We consider a cubic nonlinear wave equation on a network and show that inspecting the normal modes of the graph, we can immediately identify which ones extend into nonlinear periodic orbits. Two main classes of nonlinear periodic orbits…
This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the…
We study phase transitions and the nature of order in a class of classical generalized $O(N)$ nonlinear $\sigma$-models (NLS) constructed by minimally coupling pure NLS with additional degrees of freedom in the form of (i) Ising…
Nonlinear phononics is the phenomenon in which a coherent dynamics in a material along a set of phonons is launched after its infrared-active phonons are selectively excited using external light pulses. The microscopic mechanism underlying…
We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond to harmonic forcing. This approach reconciles the…
We study the complex nonlinear dynamics of the two-photon Dicke model in the semiclassical limit by considering cavity and qubit dissipation. In addition to the normal and super-radiant phases, another phase that contains abundant…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
This paper considers a class of nonlinear time harmonic Maxwell systems at fixed frequency, with nonlinear terms taking the form $\mathscr{X}(x,|\vec E(x)|^2)\vec E(x)$, $\mathscr{Y}(x,|\vec H(x)|^2)\vec H(x)$, such that $\mathscr{X}(x,s)$,…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone…
We investigate second-order nonlinear processes in a system of two coupled identical optical micro-resonators. The double resonance and phase-matching conditions are simultaneously obtained thanks to the frequency splitting induced by the…
The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…
A theory of weakly-nonlinear low-temperature relaxational absorption of acoustic and electromagnetic waves in dielectric and metallic glasses is developed. Basing upon the model of two-level tunneling systems we show that the nonlinear…
The paper investigates nonlinear control laws obtained from linear one by two types of substitutions using odd functions. The first substitution consists in passing each component of the state vector through a nonlinear function, the second…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…