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It is now well established that photonic systems can exhibit topological energy bands. Similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against backscattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a nonzero topological invariant guarantees the presence of a parametrically unstable chiral edge mode in a system with boundaries, even though there are no bulk-mode instabilities. We show that one can exploit this to realize a topologically protected, quantum-limited traveling wave parametric amplifier. The device is naturally protected against both internal losses and backscattering; the latter feature is in stark contrast to standard traveling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.

Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. Here we develop a dual-pump, broadband Josephson travelling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing on par with the best resonator-based squeezers. We also demonstrate two-mode squeezing at microwave frequencies with bandwidth in the gigahertz range that is almost two orders of magnitude wider than that of contemporary resonator-based squeezers. Our amplifier is capable of simultaneously creating entangled microwave photon pairs with large frequency separation, with potential applications including high-fidelity qubit readout, quantum illumination and teleportation.Parametric amplifiers are a key component in the operation and readout of superconducting quantum circuits. An improved travelling-wave amplifier design enables broadband squeezing and high-performance operation.

Wavelength division multiplexing (WDM) is a very important technique to utilize the bandwidth of optical fiber; multiple channels can be transmitted in the same fiber cable at the same time, and each channel has individual wavelength. At different network node, it’s required to add or drop wavelength, wavelength converter process is a technique responsible for converting the wavelength of signal to other wavelength up or down from the original value. This paper has presented a proposed model to generate inverted and non-inverted wavelength conversion by using single wide band traveling wave semiconductor optical amplifier (WBSOA), based on cross-gain modulation. The investigation of conversion efficiency ( ) and quality factor ( ), versus pump power ranged value from −30 to 0 dB m, and input signal power is 0 dB m with data rate 25 Gb/s, are studied for up and down-wavelength conversion, “co-propagation” and “counter-propagation”, respectively. The simulation results indicate that, to get maximum conversion efficiency and maximum quality factor by using single WBSOA, the pump power should be located between −30 to −20 dB m for maximum conversion efficiency and equal to −10 dB m for maximum quality factor, that for up- and down-wavelength conversion, co-propagation and counter-propagation.

In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

The Kadomtsev–Petviashvili equation used in this article is used to model shallow water waves with weakly nonlinear restorative forces as well as waves in a strong magnetic medium. The bilinear form of the equation is constructed and several new exact solutions are discovered using the ansatz as an exponential function and the new homoclinic approach based on the Hirota bilinear form. The exact solutions as seen in the three-dimensional graphs indicate the evolution of periodic properties. In this article, the modulation instability is applied to study stability of the solutions. For this evolution equation, the findings revealed new mechanical structures as well as new properties. In this article, 3D, density graphs and some physical dynamics of traveling wave solutions produced by the newly proposed homoclinic approach to strengthen the Hirota bilinear method are analyzed. All of the discovered solutions are put into the equation to ensure their existence. The connection between the wave’s phase velocity and the number of waves is discussed by means of traveling wave solutions that allow the discussion of the phenomenon of dispersion of a wave. Also, taking into account the newly discovered traveling wave solutions for the Kadomtsev–Petviashvili equation, the propagation of the traveling wave in the direction of x and y is studied. These findings provide us a fresh doorway for us to examine the model in deep. The existing work is widely used to report a variety of fascinating physical occurrences in the domains of shallow water waves, ferromagnetic mediums, and other similar phenomena.

We focus on a class of generalized Burgers Huxley equation and its singularly perturbed form, which has significant impacts on practical applications. The existence of different traveling wave solutions is established. Numerical examples are conducted to provide more intuitive illustrations of our analytical results. Our analysis is based on the combination of geometric singular perturbation theory, invariant manifold theory and bifurcation theory.

In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'.

This paper summarizes the research status of hidden danger early-warning for transmission lines, analyzes the existing research methods and applications of hidden dangers such as tree-related ones, bird nests on lines, and foreign objects attached to conductors, and proposes a new early-warning method based on the traveling-wave discharge characteristics. Through simulation experiments, the discharge waveforms of tree-related hidden dangers at different distances are obtained. The distribution of characteristic parameters of the discharge waveforms in different development stages of trees is studied. Four characteristic parameters, namely amplitude, number of pulses, pulse energy, and phase interval, are calculated and assigned values one by one. The results show that when the net distance between the tree and the line gradually decreases, the discharge amplitude, the number of discharge pulses, the discharge pulse energy, and the initial discharge phase difference generally show an increasing trend, and this increasing trend is more obvious at higher voltage levels. The main frequency of tree discharge pulses presents a wavy-line distribution, mostly concentrated within 1-2 MHz. Therefore, the discharge risk level of tree-related hidden dangers can be calculated according to the discharge data characteristics of trees in different development stages, realizing the hierarchical early-warning of tree-related hidden dangers.

In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system. To investigate the potential presence of chaotic behaviors, we introduce a perturbed term into the dynamical system and systematically analyze the extended nonlinear Schrödinger equation. This investigation is further enriched by the presentation of comprehensive two- and 3D phase portraits. Moreover, we conduct a meticulous sensitivity analysis of the dynamical system using the Runge–Kutta method. Through this analytical process, we confirm that minor fluctuations in initial conditions have only minimal effects on solution stability. Additionally, we utilize the complete discrimination system of the polynomial method to systematically construct single traveling wave solutions for the governing model.

In this paper travelling waves with distributional profiles for the Camassa–Holm equation are studied. Using a product of distributions a new solution concept is introduced which extends the classical one. As a consequence, necessary and sufficient conditions for the propagation of a distributional profile are established and we present examples with discontinuous solutions, measures and even distributions that are not measures. One of these examples may be interpreted as a simple model for a “tsunami” in the setting of shallow water theory. We also prove that, under natural assumptions, profiles belonging to the Sobolev space H loc 1 ( R ) usually considered in the classical weak formulation can be seen as particular cases of our distributional solution concept.