The main novelty of this paper lies in five aspects: (1) To our best knowledge, the modified
G
′
G
2
-expansion method was firstly applied in nonlinear q-deformed Sinh–Gordon equation (NQSGE). (2) ...The effects of wave obliqueness about NQSGE are firstly discussed in this paper which did not happen in previous papers. (3) Phase portraits and bifurcation behaviors about NQSGE are also firstly investigated in Hamiltonian system that did not appear in previous studies. (4) Sensitive analysis to initial value and chaotic behavior are also firstly studied in NQSGE. (5) The modified Riemann–Liouville, Beta, Conformable and M-truncated fractional derivatives are tested for accuracy in Fig. 18a, b. To our best knowledge, we seem firstly compare the relations and distinctions among different fractional-order derivatives in NQSGE model. The generalizations (1)–(5) indicated that the wave propagation of solitions about NQSGE model is mastered by the changed fraction, changed wave obliqueness angle and other physical factors.
The nonlinear Schrodinger equation (NLSE) in (2 + 1) dimensions with beta derivative evolution is considered here to study nonlinear coherent structures for Heisenberg models of ferromagnetic spin ...chain with magnetic exchanges. Such structures are studied by determining the analytical solutions of NLSE having beta derivative evolution via two different mathematical techniques. The dynamical behaviors of equilibrium points are also studied by deriving the planar dynamical system from the considered equation. Some of obtained analytical solutions are described with graphical representation by varying beta derivative parameter (BDP) and obliqueness. It is revealed that the obliqueness is extensively affected both on the plane wave dynamics as well as equilibrium points of the system, whereas the equilibrium points are independent of BDP.
Abstract We propose that gamma-ray burst (GRB) pulses are produced when highly relativistic jets sweep across an observer’s line of sight. We hypothesize that axisymmetric jet profiles, coupled with ...special relativistic effects, produce the time-reversed properties of GRB pulses. Curvature resulting from rapid jet expansion is responsible for much of the observed pulse asymmetry and hard-to-soft evolution. The relative obliqueness with which the jet crosses the line of sight explains the known GRB pulse morphological types. We explore two scenarios: one in which a rigid/semirigid jet moves laterally and another in which a ballistic jet sprays material from a laterally moving nozzle. The ballistic jet model is favored based upon its consistency with standard emission mechanisms.
With decreasing Reynolds number,
$Re$
, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here ...the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of
$Re$
lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.
The study aims to explore obliquely propagating optical wave solutions to the (2 + 1)-dimensional chiral nonlinear Schrödinger (NLS) equation in both the absence and presence of the Atangana ...derivative. In order to convert the classical-order chiral nonlinear Schrödinger equation to an ordinary differential equation, a transformation associated with wave obliqueness is applied. Hereafter, the unified method is applied to the reduced equation. As outcomes, the dark, periodic singular with unequal wave length, periodic with equal wavelength, periodic, unsmooth periodic, singular periodic soliton solutions are received to the ordinary differential equation. Later, the acquired solutions are then put to the applied transformation associated with obliqueness. Moreover, the fractional-order chiral NLS equation is solved by using the spatiotemporal Atangana derivative with oblique wave transformation and the unified method. In terms of wave obliqueness, fractionality, and applied technique sense, all generated wave solutions are revealed to be novel. Along with their physical explanations, the impacts of obliqueness and fractionality on the solutions are graphically illustrated. It is exposed that as obliqueness and fractionality increase, the optical wave phenomena change. Additionally, it is discovered that the employed method can be used to obtain novel optical soliton features to the chiral nonlinear Schrödinger equation with or without fractional and obliqueness constraints. It can be assured that the utilized method is more powerful than the other methods. As a result, the method can be used in future research to explain the many physical phenomena that arise in optical fiber communication networks.
We investigate through the ansatz and auxiliary equation methods novel types of solitary wave solutions for (2+1)-D coupled nonlinear electrical transmission lattice with wave obliqueness. While ...including the fractional conformable derivatives in addition to the wave obliqueness parameter, we turn the fractional circuit equation into an ordinary differential equation. Therefore, we explore some fractional alphabetic and exotic solitons, solutions of the equation governing the dynamics of the voltage wave for the studied model. With the graphical representation of the novel obtained solutions, we highlight the effects of the fractional order and the wave obliqueness parameter. From the physical parameters of the circuit and the wave obliqueness parameter we examine the stationary points.
Accurate modeling of wave‐particle interactions in the radiation belts requires detailed information on wave amplitudes and wave‐normal angular distributions over L shells, magnetic latitudes, ...magnetic local times, and for various geomagnetic activity conditions. In this work, we develop a new and comprehensive parametric model of VLF chorus waves amplitudes and obliqueness in the outer radiation belt using statistics of VLF measurements performed in the chorus frequency range during 10 years (2001–2010) aboard the Cluster spacecraft. We used data from the Spatio‐Temporal Analysis of Field Fluctuations‐Spectrum Analyzer experiment, which spans a total frequency range from 8 Hz to 4 kHz. The statistical model is presented in the form of an analytical function of latitude and Kp (or Dst) index for day and night sectors of the magnetosphere and for two ranges of L shells above the plasmapause, from L = 4 to 5 and from L = 5 to 7. This model can be directly applied for numerical calculations of charged particle pitch angle and energy diffusion coefficients in the outer radiation belt, allowing to study with unprecedented detail their statistical properties as well as their important spatiotemporal variations with geomagnetic activity.
Key Points
The model for chorus wave amplitude and obliqueness is presented
Input parameters for the model are Kp index, geomagnetic latitude, MLT, and L shell
The model can be directly applied for diffusion rates calculation
The detailed energy sources that sustain the eigenmodal exponential growth in boundary layers are currently unclear. In the present study, the phase of each term in the linear stability equation is ...examined to identify the significant physical sources for a wide range of Mach numbers and wall temperature ratios. The Tollmien–Schlichting mode for incompressible flows, the oblique first mode for supersonic flows and the Mack second mode and supersonic mode for hypersonic flows share some similar features. The unique appearance of obliqueness for the most unstable first mode is accompanied by the enhancement of Reynolds shear stress. By contrast, the weakened Reynolds thermal stress prevents the oblique second mode from being the most unstable state. Wall cooling stabilises the oblique first mode by rendering Reynolds thermal stress and dilatation fluctuations out of phase with the internal energy fluctuation. It destabilises the second mode by a newly generated pronounced region of wall-normal internal energy transport beneath the second generalised inflection point. In comparison, the porous coating destabilises the oblique first mode by significantly enhancing the mean-shear production while it stabilises the second mode similarly to wall heating. Finally, the relatively weak supersonic mode has the feature that the phase destruction of wall-normal transport near the critical layer results in a low contribution to the internal energy growth. Connections and consistencies are also highlighted with the previous inviscid thermoacoustic interpretation for the second mode (Kuehl, AIAA J., vol. 56, 2018, pp. 3585–3592) and for the supersonic mode. The pronounced sources along the critical layer and near-wall regions provide a unified understanding of the local energy amplification mechanisms of the inviscid modes in hypersonic boundary layers.
PDF
