Search Results (9)

The goal of this research is to utilize some ansatz forms of solutions to obtain novel forms of soliton solutions for the Benney–Luke equation. It is a mathematically valid approximation that describes the propagation of two-way water waves in the presence of surface tension. By using ansatz forms of solutions, with an appropriate set of parameters, the lump soliton, periodic cross-kink waves, multi-waves, breather waves, Ma-breather, Kuznetsov–Ma-breather, periodic waves and rogue waves solutions can be obtained. Breather waves are confined, periodic, nonlinear wave solutions that preserve their amplitude and shape despite alternating between compression and expansion. For some integrable nonlinear partial differential equations, a lump soliton is a confined, stable solitary wave solution. Rogue waves are unusually powerful and sharp ocean surface waves that deviate significantly from the surrounding wave pattern. They pose a threat to maritime safety. They typically show up in solitary, seemingly random circumstances. Periodic cross-kink waves are a particular type of wave pattern that has frequent bends or oscillations that cross at right angles. These waves provide insights into complicated wave dynamics and arise spontaneously in a variety of settings. In order to predict the wave dynamics, certain 2D, 3D and contour profiles are also analyzed. Since these recently discovered solutions contain certain arbitrary constants, they can be used to describe the variation in the qualitative characteristics of wave phenomena. Full article

This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin–Bona–Mahony–Peregrine–Burgers (BBMPB) equation. The various types of wave structures are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave, and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately find solutions and predict the behaviour of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behaviour of the solutions, some 3D plots and their respective contour level are shown, choosing different values of the parameters. Full article

In the present paper, we describe a 2.5D (two-and-a-half-dimensional) magnetohydrodynamic (MHD) simulation that provides a detailed picture of the evolution of cool jets triggered by initial vertical velocity perturbations in the solar chromosphere. We implement random multiple velocity, $V_y$, pulses of amplitude 20–50 km s${}^{-1}$ between 1 Mm and 1.5 Mm in the Sun’s atmosphere below its transition region (TR). These pulses also consist of different switch-off periods between 50 s and 300 s. The applied vertical velocity pulses create a series of magnetoacoustic shocks steepening above the TR. These shocks interact with each other in the inner corona, leading to complex localized velocity fields. The upward propagation of such perturbations creates low-pressure regions behind them, which propel a variety of cool jets and plasma flows in the localized corona. The localized complex velocity fields generate transverse oscillations in some of these jets during their evolution. We study the transverse oscillations of a representative cool jet J${}_1$, which moves up to the height of 6.2 Mm above the TR from its origin point. During its evolution, the plasma flows make the spine of jet J${}_1$ radially inhomogeneous, which is visible in the density and Alfvén speed smoothly varying across the jet. The highly dense J${}_1$, which is triggered along the significantly curved magnetic field lines, supports the propagating transverse wave of period of approximately 195 s with a phase speed of about 125 km s⁻¹. In the distance–time map of density, it is manifested as a transverse kink wave. However, the careful investigation of the distance–time maps of the x- and z-components of velocity reveals that these transverse waves are actually of mixed Alfvénic modes. The transverse wave shows evidence of damping in the jet. We conclude that the cross-field structuring of the density and characteristic Alfvén speed within J${}_1$ causes the onset of the resonant conversion and leakage of the wave energy outward to dissipate these transverse oscillations via resonant absorption. The wave energy flux is estimated as approximately of 1.0 × 10${}^6$ ergs cm${}^{-2}$ s${}^{-1}$. This energy, if it dissipates through the resonant absorption into the corona where the jet is propagated, is sufficient energy for the localized coronal heating. Full article

We explore stochastic–fractional Drinfel’d–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution. We also examine some M-shaped solutions such as the M-shaped rational solution, M-shaped rational solution with one and two kink waves. We also derive the M-shaped interaction with rogue and kink waves and the M-shaped interaction with periodic and kink waves. This model is used in mathematical physics, surface physics, plasma physics, population dynamics and applied sciences. Moreover, we also show our results graphically in different dimensions. We obtain these solutions under some constraint conditions. Full article

We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots. Full article

The purpose of this review is to describe the physical mechanism responsible for the appearances of both traveling and non-traveling distortions in a twisted microsized nematic volume under the effect of a large electric field. Both experimental and theoretical works devoted to the excitation of structured periodic domains in initially homogeneously aligned liquid crystal systems under the effects of strong crossed electric and magnetic fields were analyzed. Electrically driven distortions in the microfluidic nematic capillary in the presence of a temperature gradient in it, based on the number of numerical results, were analyzed. We also focus on the description and explanation of the novel mechanism of excitation of the kink- and $\pi$-like distortion waves of the director field $\widehat{\mathbf{n}}$ in a cylindrical nematic micro-volume under the effect of voltage U and temperature gradient $\nabla T$, set up between the cooler inner and hotter outer cylinders. Electrically driven torsional distortions in twisted nematic micro-volumes in the form of the kink-like running front based on the classical Ericksen–Leslie approach were considered. Full article

This manuscript consist of diverse forms of lump: lump one stripe, lump two stripe, generalized breathers, Akhmediev breather, multiwave, M-shaped rational and rogue wave solutions for the complex cubic quintic Ginzburg Landau (CQGL) equation with intrapulse Raman scattering (IRS) via appropriate transformations approach. Furthermore, it includes homoclinic, Ma and Kuznetsov-Ma breather and their relating rogue waves and some interactional solutions, including an interactional approach with the help of the double exponential function. We have elaborated the kink cross-rational (KCR) solutions and periodic cross-rational (KCR) solutions with their graphical slots. We have also constituted some of our solutions in distinct dimensions by means of 3D and contours profiles to anticipate the wave propagation. Parameter domains are delineated in which these exact localized soliton solutions exit in the proposed model. Full article

In this work, we study a time-fractional ion sound and Langmuir waves system (FISLWS) with Atangana–Baleanu derivative (ABD). We use a fractional ABD operator to transform our system into an ODE. We investigate multiwaves, periodic cross-kink, rational, and interaction solutions by the combination of rational, trigonometric, and various bilinear functions. Furthermore, 3D, 2D, and relevant contour plots are presented for the natural evolution of the gained solutions under the selection of proper parameters. Full article