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Three-wave resonant interactions are commonly observed in the dispersive and weakly nonlinear media in fluid mechanics, plasma physics, nonlinear optics, solid-state physics, Bose–Einstein condensates and acoustics. This paper investigates a three-wave resonant interaction system in the one-dimensional space-time form. For that system of the soliton-exchange case, a Lax pair is introduced. Then, we utilize the generalized Darboux transformation method to derive the semi-rational solutions depicting the bound-state dark–bright mixed solitons. The three wave packets can manifest themselves as the bound-state bright–dark–bright solitons on the zero–nonzero–zero background, and bound-state dark–bright–bright solitons on the nonzero–zero–zero background. The bound states between the bright/dark solitons exhibit periodic attractions and repulsions, while the bound states among the bright/dark solitons and multi-pole bright/dark solitons exhibit non-periodic attractions and repulsions. We explore how the phase shift of the single bright/dark soliton component affects the bound states among a single bright/dark soliton and the double-pole bright/dark solitons. All the results obtained for the one-dimensional space-time evolution can be reinterpreted in terms of the two-dimensional steady-state interaction. This work may provide explanations for the complex and variable natural mechanisms of three-wave resonant interactions in various physical contexts.

In this paper, a second-order three-wave interaction system, which belongs to a three-wave resonant interaction hierarchy, is investigated. Based on a known Lax pair, we firstly derive a binary Darboux transformation and the N th-order analytic solutions with symbolic computation, where N is a positive integer. Behaviors of the one soliton are studied, and then, multi solitons and bound-state solitons on the zero background are investigated. When we select two of the three seed solutions as 0, the N th-order analytic solutions describe the interactions among the breathers and three kinds of the dark-bright solitons. Moreover, we explore the influence of certain parameters on the interactions among the breathers and three kinds of the dark-bright solitons. With less than two of the three seed solutions selected as 0, the breathers and bound-state breathers are derived via the N th-order analytic solutions.

We study the influence of real structure of electromagnetic ion-cyclotron wave packets in the Earth’s radiation belts on precipitation of relativistic electrons. Automatic algorithm is used to distinguish isolated elements (wave packets) and obtain their amplitude and frequency profiles from satellite observations by Van Allen Probe B. We focus on rising-tone EMIC wave packets in the proton band, with a maximum amplitude of 1.2–1.6 nT. The resonant interaction of the considered wave packets with relativistic electrons 1.5–9 MeV is studied by numerical simulations. The precipitating fluxes are formed as a result of both linear and nonlinear interaction; for energies 2–5 MeV precipitating fluxes are close to the strong diffusion limit. The evolution of precipitating fluxes is influenced by generation of higher-frequency waves at the packet trailing edge near the equator and dissipation of lower-frequency waves in the He+ cyclotron resonance region at the leading edge. The wave packet amplitude modulation leads to a significant change of precipitated particles energy spectrum during short intervals of less than 1 minute. For short time intervals about 10–15 s, the approximation of each local amplitude maximum of the wave packet by a Gaussian amplitude profile and a linear frequency drift gives a satisfactory description of the resonant interaction.

In a two-layer meta surface consisting of periodically arranged rods, there is a strong dispersion of the transmission coefficient in the microwave region of the spectrum. The observed phenomenon is the result of the resonant interaction of the microwave with the rod, where a standing wave with axial symmetry is formed, as well as the effective electrical interaction between the rods of adjacent layers. The transmission coefficient curve found in the experiment has an acute peak, which allows the structure to be used as a bandpass filter. It was found that the resonant frequency shifts to the low-frequency region as the length of the rods, their diameter, and the distance between the layers increases, which opens up the possibilities of controlling the microwave.

Through the emission of high‐frequency radio waves, ground‐based heating facilities can generate Extremely‐Low‐Frequency (ELF) and Very‐Low‐Frequency (VLF) waves in the ionosphere, a portion of which can penetrate into the Earth's radiation belts and influence the electron population therein. Although various measurements of ELF/VLF waves generated by ionospheric heating experiments have been reported, combined analysis using both observations and simulations remain quite limited and, thus, the underlying effects of these experiments are not well understood. In this study, we quantify these effects using measurements of plasma waves and high‐energy electrons during the joint experiment conducted between the China Seismo‐Electromagnetic Satellite (CSES) and the ionospheric heater SURA on 17 November 2021. We show that SURA‐generated ELF/VLF waves are mostly in the frequency range of 1–5 kHz as measured by CSES, with an amplitude of ∼50 pT at 0.8–2 kHz. The overall structure is similar to previous measurements of ELF/VLF waves generated by the High‐Frequency Active Auroral Research Program (HAARP). These waves can, in principle, influence electrons in the 100–250 keV energy range, mostly via pitch‐angle diffusion. On basis of further simulations of the evolution of electron phase space density under the impact of SURA‐generated ELF/VLF waves, our modeling output shows favorable consistency with the electron flux variations measured by CSES. Our results support a causative relation between the SURA heating experiment and the CSES‐observed dynamics of ELF/VLF waves and energetic electrons, which has important implications to further our understanding of the near‐Earth space environment and to develop artificial radiation belt remediation techniques.

Models describing long wave–short wave resonant interactions have many physical applications, from fluid dynamics to plasma physics. We consider here the Yajima–Oikawa–Newell (YON) model, which was recently introduced, combining the interaction terms of two long wave–short wave, integrable models, one proposed by Yajima–Oikawa, and the other one by Newell. The new YON model contains two arbitrary coupling constants and it is still integrable—in the sense of possessing a Lax pair—for any values of these coupling constants. It reduces to the Yajima–Oikawa or the Newell systems for special choices of these two parameters. We construct families of periodic and solitary wave solutions, which display the generation of very long waves. We also compute the explicit expression of a number of conservation laws.

This paper proposes a 3-D non-hydrostatic free surface flow model with a newly proposed general boundary-fitted grid system to simulate the nonlinear interactions of the bi-chromatic deep-water gravity waves. First, the monochromatic bidirectional and bi-chromatic bidirectional waves of small wave steepness are successively simulated to verify the abilities of the numerical model. Then, a series of bi-chromatic progressive waves of moderate wave steepness and different crossing angles are simulated and analyzed in detail. It is found that if the crossing angle is close to or smaller than the resonant angle, apparent discrepancies are observed among the numerical results, the linear wave theory, and the steady third-order theory. Otherwise, the three solutions coincide well. Through analysis, it is concluded that the discrepancies are caused by the third-order quasi-resonant interactions between the bi-chromatic progressive waves. Such interactions not only could modify the wave spectrum, but could also change the wave shape patterns.

The emergence of quasiparticles in interacting matter represents one of the cornerstones of modern physics. However, in the vicinity of a quantum critical point, the existence of quasiparticles comes under question. Here, we created Bose polarons near quantum criticality by immersing atomic impurities in a Bose-Einstein condensate (BEC) with near-resonant interactions. Using radiofrequency spectroscopy, we probed the energy, spectral width, and short-range correlations of the impurities as a function of temperature. Far below the superfluid critical temperature, the impurities formed well-defined quasiparticles. Their inverse lifetime, given by their spectral width, increased linearly with temperature at the so-called Planckian scale, consistent with quantum critical behavior. Close to the BEC critical temperature, the spectral width exceeded the impurity’s binding energy, signaling a breakdown of the quasiparticle picture.

Investigating the wave hydrodynamics of free-surface flow over rippled bottoms is a continuing concern due to the existence of submarine multiple sandbars and ambient flow in coastal and estuarial areas. More attention to free-surface wave stimulation has been received from the perspective of resonant wave-wave interaction, which is an intensive way for wave energy transfer and a potential way for wave component generation. However, the basic behavior of the triad resonant interaction of this problem is still limited and unclear. In this study, the triad resonant interaction induced by steady free-surface flow over rippled bottoms is numerically investigated by means of the High-Order Spectral (HOS) method. By considering the interactions among free-surface waves, ambient current, and rippled bottoms, the numerical model is applied for this situation based on Zakharov equation with ambient flow term. The temporal evolution of the triad resonant wave amplitude has been numerically investigated and compared well with multiple-scale expansion perturbation theory. Specifically, the temporal evolution behaviors of all six triad resonant wave components are confirmed by both numerical simulation and nonlinear perturbation analysis.

The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully nonlinear numerical studies have indicated that the amplification can exceed 3, but its physical mechanism has not been clarified. This study shows that spectral broadening, bound-wave production, and phase convergence are essential to crest enhancement beyond the AB solution. The free-wave spectrum of modulated wave trains broadens owing to nonlinear quasi-resonant interaction. This enhances bound-wave production at high wavenumbers. The phases of all the wave components nearly coincide at peak modulation and enhance amplification. This study found that the phase convergence observed in linear-focusing waves can also occur due to nonlinear wave evolution. These findings are obtained by numerically investigating the modulated wave trains using the higher-order spectral method (HOSM) up to the fifth order, which allows investigations of nonlinearity and spectral bandwidth beyond the NLSE framework. Moreover, the crest enhancement is confirmed through a tank experiment wherein waves are generated in the transition region from non-breaking to breaking. Owing to strong nonlinearity, the maximum crest height observed in the tank begins to exceed the HOSM prediction at an initial wave steepness of 0.10.