12,146 research outputs found

    A computational study on the effects of fast-rising voltage on ionization fronts initiated in sub-mm air and CO2 gaps

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    Gas discharge and breakdown phenomena have become increasingly important for the development of an ever-growing number of applications. The need for compact and miniaturized systems within power, pulsed power, semiconductor, and power electronic industries has led to the imposing of significant operating electric field stresses on components, even within applications with low operating voltages. Consequently, the interest in gas discharge processes in sub-millimeter and microscale gaps has grown, as the understanding of their initiation and propagation is critical to the further optimization of these technologies. In this work, a computational study of primary ionization fronts has been conducted, which systematically investigated the role of voltage rate-of-rise in point-plane and point-point electrode geometries with an inter-electrode gap maintained at 250 μm and a needle radius of 80 μm. Using the hydrodynamic approach with the local mean energy approximation, along with simplified plasma chemistry, simulations have been performed under positive and negative ramp voltages, rising at 50, 25, 16.67, 12.5, and 10 kV/ns in synthetic air and in pure CO2. Results on the developed electric field, electron densities, and propagation velocities are presented and discussed. Effects on the cathode sheath thickness scaling with voltage rate-of-rise have been additionally analyzed, the mechanisms behind these effects and their potential impacts are discussed. The work conducted in this study contributes towards an increased understanding of the gas discharge process, under fast-transients and nonuniform electric fields, with relevance to microelectromechanical, power, and pulsed power system design

    Solitons in magneto-optic waveguides with Kudryashov’s law nonlinear refractive index for coupled system of generalized nonlinear Schrödinger’s equation using modified extended mapping method

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    In this work, we investigate the optical solitons and other waves through magneto-optic waveguides with Kudryashov’s law of nonlinear refractive index in the presence of chromatic dispersion and Hamiltonian-type perturbation factors using the modified extended mapping approach. Many classifications of solutions are established like bright solitons, dark solitons, singular solitons, singular periodic wave solutions, exponential wave solutions, rational wave, solutions, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic function solutions. Some of the extracted solutions are described graphically to provide their physical understanding of the acquired solutions

    Modulational instability windows in the nonlinear Schrödinger equation involving higher-order Kerr responses

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    We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schrödinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of multiple regimes of stability and instability of plane-wave solutions in such systems. Moreover, we discuss a new parametric regime in the higher-order Kerr response, which allows for the observation of several, alternating stability-instability windows defining a yet unexplored instability landscape.Xunta de Galicia | Ref. EM2013/00

    Unification of Adomian decomposition method and ZZ transformation for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems

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    This paper presents a novel approach for exploring the dynamics of fractional Kersten-Krasil'shchik coupled KdV-mKdV systems by using the unification of the Adomian decomposition method and ZZ transformation. The suggested method combines the Aboodh transform and the Adomian decomposition method, both of which are trustworthy and efficient mathematical tools for solving fractional differential equations (FDEs). This method's theoretical analysis is addressed for nonlinear FDE systems. To find exact solutions to the equations, the method is applied to fractional Kersten-Krasil'shchik linked KdV-mKdV systems. The results show that the suggested method is efficient and practical for solving fractional Kersten-Krasil'shchik linked KdV-mKdV systems and that it may be applied to other nonlinear FDEs. The suggested method has the potential to provide new insights into the behavior of nonlinear waves in fluid and plasma environments, as well as the development of new mathematical tools for modeling and studying complicated wave phenomena

    Exact Jacobi elliptic solutions of some models for the interaction of long and short waves

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    Some systems were recently put forth by Nguyen et al. as models for studying the interaction of long and short waves in dispersive media. These systems were shown to possess synchronized Jacobi elliptic solutions as well as synchronized solitary wave solutions under certain constraints, i.e., vector solutions, where the two components are proportional to one another. In this paper, the exact periodic traveling wave solutions to these systems in general were found to be given by Jacobi elliptic functions. Moreover, these cnoidal wave solutions are unique. Thus, the explicit synchronized solutions under some conditions obtained by Nguyen et al. are also indeed unique

    On numerical and analytical solutions of the generalized Burgers-Fisher equation

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    In this paper, the semi-analytic iterative and modified simple equation methods have been implemented to obtain solutions to the generalized Burgers-Fisher equation. To demonstrate the accuracy, efficacy as well as reliability of the methods in finding the exact solution of the equation, a selection of numerical examples was given and a comparison was made with other well-known methods from the literature such as variational iteration method, homotopy perturbation method and diagonally implicit Runge-Kutta method. The results have shown that between the proposed methods, the modified simple equation method is much faster, easier, more concise and straightforward for solving nonlinear partial differential equations, as it does not require the use of any symbolic computation software such as Maple or Mathematica. Additionally, the iterative procedure of the semi-analytic iterative method has merit in that each solution is an improvement of the previous iterate and as more and more iterations are taken, the solution converges to the exact solution of the equation

    Stability and dynamics of regular and embedded solitons of a perturbed Fifth-order KdV equation

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    Families of symmetric embedded solitary waves of a perturbed Fifth-order Korteweg–de Vries (FKdV) system were treated in Choudhury et al. (2022) using perturbative and reversible systems techniques. Here, the stability of those solutions, which was not considered in the earlier paper, is detailed. In addition, the results of Choudhury et al. (2022) are extended to the case of asymmetric solitary waves, as well as their stability. Finally, other novel multi-humped regular solitary waves of this system are derived using convergent infinite series solutions for the homoclinic orbits of the FKdV-traveling wave equatio

    Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+1)-dimensions with gas bubbles in hydrodynamics and fluids

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    Nonlinear evolution equations (NLEEs) are frequently employed to determine the fundamental principles of natural phenomena. Nonlinear equations are studied extensively in nonlinear sciences, ocean physics, fluid dynamics, plasma physics, scientific applications, and marine engineering. The generalized exponential rational function (GERF) technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in (3+1) dimensions, which explains several more nonlinear phenomena in liquids, including gas bubbles. A large number of closed-form wave solutions are generated, including trigonometric function solutions, hyperbolic trigonometric function solutions, and exponential rational functional solutions. In the dynamics of distinct solitary waves, a variety of soliton solutions are obtained, including single soliton, multi-wave structure soliton, kink-type soliton, combo singular soliton, and singularity-form wave profiles. These determined solutions have never previously been published. The dynamical wave structures of some analytical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters. This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics, fluid dynamics, and other fields of nonlinear sciences
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