Search Results (5)

The time-fractional coupled Drinfel’d–Sokolov–Wilson (DSW) equation is pivotal in soliton theory, especially for water wave mechanics. Its precise description of soliton phenomena in dispersive water waves makes it widely applicable in fluid dynamics and related fields like tsunami prediction, mathematical physics, and plasma physics. In this study, we present novel soliton solutions for the DSW equation, which significantly enhance the accuracy of describing soliton phenomena. To achieve these results, we employed two distinct methods to derive the solutions: the Sardar subequation method, which works with one variable, and the $\left(\frac{{\mathsf{\Omega }}^{\prime }}{\mathsf{\Omega }}, \frac{1}{\mathsf{\Omega }}\right)$ method which utilizes two variables. These approaches supply significant improvements in efficiency, accuracy, and the ability to explore a broader spectrum of soliton solutions compared to traditional computational methods. By using these techniques, we construct a wide range of wave structures, including rational, trigonometric, and hyperbolic functions. Rigorous validation with Mathematica software 13.1 ensures precision, while dynamic visual representations illustrate soliton solutions with diverse patterns such as dark solitons, multiple dark solitons, singular solitons, multiple singular solitons, kink solitons, bright solitons, and bell-shaped patterns. These findings highlight the effectiveness of these methods in discovering new soliton solutions and supplying deeper insights into the DSW model’s behavior. The novel soliton solutions obtained in this study significantly enhance our understanding of the DSW equation’s underlying dynamics and offer potential applications across various scientific fields. Full article

The work is devoted to the results of processing electromagnetic radiation signals obtained during laboratory loading of marble and diabase samples using a technique for determining the parameters of microcracks, developed and published by the author earlier. As a result of such processing, certain patterns were found in the nature of the evolution of the oscillatory process ensemble of microcracks. For example, solitary non-linear waves almost always preceded a sequence of High Frequency traces. Equations for straight lines approximating High Frequency traces in logarithmic coordinates, close to the equation of the Gutenberg–Richter law. Due to the similarity of seismic processes at different scale levels, the results of modeling at the microscale level can be used to describe seismic processes at the macroscale level, for example, to study the processes occurring immediately before destruction and at the time of destruction in order to search for repeatability and regularities. The regularities obtained can be used in the development of a predictive criterion that makes it possible to predict the time of one or another geophysical (seismic) event. Full article

Fluctuations of sound intensity in the presence of moving nonlinear internal waves (NIWs) are studied. Prior works revealed the existence of peaks in the spectrum of these fluctuations due to mode coupling. In the given paper, the results of experiment ASIAEX 2001 are considered. Episodes are analyzed when soliton-like NIW move for ~6 h approximately along an acoustic track of length ~30 km. The depth of the ocean changes from ~350 m (position of the source) up to ~120 m near the receiver (Vertical Line Array). The source, placed near the bottom, transmitted pulses (M-sequences) with a frequency of 224 Hz. Theoretical analysis and numerical modeling show that peak frequencies in the spectrum of intensity fluctuations correspond to the most strongly interacting pairs of modes: in the given case pairs 2–3 and 3–4 and values of dominating frequencies are determined by the spatial scale of interference beating Λ of coupling modes and by the speed v of NIW. Due to the fact that in the narrowing channel velocity v decreases as well as the value of Λ, the predominant frequency as a function of time remains approximately the same. Results of modeling are in a good agreement with experimental data. Full article

Optical frequency combs (OFCs) generated in microresonators with whispering gallery modes are demanded for different applications including telecommunications. Extending operating spectral ranges is an important problem for wavelength-division multiplexing systems based on microresonators. We demonstrate experimentally three spectrally separated OFCs in the C-, U-, and E-bands in silica microspheres which, in principle, can be used for telecommunication applications. For qualitative explanation of the OFC generation in the sidebands, we calculated gain coefficients and gain bandwidths for degenerate four-wave mixing (FWM) processes. We also attained a regime when the pump frequency was in the normal dispersion range and only two OFCs were generated. The first OFC was near the pump frequency and the second Raman-assisted OFC with a soliton-like spectrum was in the U-band. Numerical simulation based on the Lugiato–Lefever equation was performed to support this result and demonstrate that the Raman-assisted OFC may be a soliton. Full article

We consider the model of minimally interacting electromagnetic, gravitational and massive scalar fields free of any additional nonlinearities. In the dimensionless form, the Lagranginan contains only one parameter $\gamma ={(m\sqrt{G}/e)}^2$ which corresponds to the ratio of gravitational and electromagnetic interactions and, for a typical elementary particle, is about ${10}^{-40}$ in value. However, regular (soliton-like) solutions can exist only for $\gamma \ne 0$, so that gravity would be necessary to form the structure of an (extended) elementary particle. Unfortunately (in the stationary spherically symmetrical case), the numerical procedure breaks in the range $\gamma \le 0.9$ so that whether the particle-like solutions actually exist in the model remains unclear. Nonetheless, for $\gamma \sim 1$ we obtain, making use of the minimal energy requirement, a discrete set of (horizon-free) electrically charged regular solutions of the Planck’s range mass and dimensions (“maximons”, “planckeons”, etc.). In the limit $\gamma \to \infty$, the model reduces to the well-known coupled system of the Einstein and Klein–Gordon equations. We obtain—to our knowledge—for the first time, the discrete spectrum of neutral soliton-like solutions (“mini-boson stars”, “soliton stars”, etc.) Full article