Abstract Focusing on a Schwarzschild spacetime modified by loop quantum gravity (LQG) holonomy corrections, this work explores the gravitational radiation produced by test masses in bound periodic configurations. The underlying geometry incorporates a quantum-correction parameter $q_c$ that alters the radial metric scaling while maintaining both asymptotic flatness and the classical horizon radius. The bound geodesics are systematically classified using the zoom--whirl representation labelled by three integers $(z,w,v)$. Gravitational waveforms are computed within a numerical framework that combines exact geodesic motion with the quadrupole approximation, which is suitable for extreme mass ratio inspirals. We demonstrate that the quantum corrections lead to distinct phase shifts, amplitude variations, and modifications to the harmonic structure of the waveforms, with increasingly complex features for orbits with larger zoom numbers. The corresponding frequency spectra and characteristic strain peak, which fall within the millihertz band, are within the sensitivity ranges of space-based detectors such as LISA, Taiji, and TianQin. For specific orbital configurations and values of the quantum-correction parameter, the characteristic strain exceeds the projected detector noise, indicating potential observability. Our results demonstrate that gravitational waves from periodic orbits provide a sensitive probe of quantum-corrected black hole spacetimes in the strong-field regime.
Abstract This study constructed the explicit N -fold Darboux transformation (DT) for the variable-coefficient nonlocal Gerdjikov–Ivanov equation based on a higher-order polynomial matrix, thereby generating various localized waves. Moreover, the generation mechanism of rogue waves (RWs) was analyzed by combining modulational instability. First, starting from a zero seed solution, N solitons and multiple solitons on the periodic background were derived using the N -fold classical DT. Analytical expressions for the amplitudes at soliton collision centers were obtained, showing that the peak amplitudes are determined only by the real parts of the spectral parameters and are independent of the variable coefficient δ ( t ) . Second, starting from a nonzero seed solution, breathers were investigated, and the first-order RW was derived by taking the limit of the first-order breather. Furthermore, the second-order RW was studied via the degenerate DT. With appropriate parameter choices, a second-order RW can split into three first-order RWs arranged in a triangular pattern. Finally, numerical simulations visually illustrated the effects of δ ( t ) on soliton interactions, soliton evolution on periodic backgrounds, breather oscillation patterns, and the spatial structures and dynamical behaviors of RWs of different orders.
Abstract Magnetized Rossby waves are low-frequency planetary waves formed by the coupling of Earth’s rotation and geomagnetic field, and their high-dimensional nonlinear theoretical system remains to be improved. Based on the geomagnetically modified dimensionless Charney equation, combined with multi-scale analysis and perturbation expansion method, this paper derives the (2+1)-dimensional Zakharov–Kuznetsov (ZK) equation for magnetized Rossby waves. The Hirota bilinear method is adopted to solve the ZK equation, and the analytical solutions of 1-soliton, 2‐soliton and 3‐soliton are obtained. Combined with the amplitude distribution and flow field characteristics, the propagation laws and evolution characteristics of solitons are systematically analyzed. Meanwhile, the influence mechanism of background flow intensity and geomagnetically modified generalized Rossby parameter on the dynamic characteristics of solitons is explored. This study further improves the high-dimensional nonlinear theoretical system of magnetized Rossby waves and can provide important theoretical support for ionospheric observation analysis and explanation of nonlinear dynamic mechanisms.
Abstract Epitaxial growth is a process in which a crystalline layer is deposited on a crystalline substrate. In this study, we investigate the nonequilibrium epitaxial growth of two-dimensional active crystals on solid substrates using Langevin dynamics simulations of purely repulsive active Brownian particles. Driven by motility-induced phase separation, the crystallization process exhibits two distinct regimes: an initial layer-by-layer deposition and subsequent interfacial growth evolution. During the initial stage, the temporal evolution of the layer coverage ratio follows a logistic-type growth curve, which is quantitatively described by a kinetic flux balance model. During the steady-state phase, a fluctuating solid–gas interface with a stable average height is formed. It is characterized by an internal dense phase, which primarily consists of a hexagonal lattice, with local topological defects near the interface. While increasing the Péclet number accelerates the initial layer coverage rate, it decreases the steady-state interfacial height and increases the bulk density of the active solid phase. Our results demonstrate that particle self-propulsion can alter the crystallization process.
Abstract In this paper, various localized wave solutions of the (2+1)-dimensional generalized nonlocal Fokas system are under investigation, through the combination of the bilinear method and long-wave limit technique. By using Hirota’s bilinear method and choosing appropriate parameters, single-periodic and two types of two-periodic wave solutions are obtained, and two-periodic waves are classified into two categories based on the positional relationships of the characteristic lines. The long-wave limit method is used to construct rational solutions, and we also analyze the dynamic characteristics of higher-order rogue waves. Furthermore, semi-rational solutions derived by the partial long-wave limit method include the following forms: (1) lumps on a dark soliton background, (2) lumps embedded in a periodic wave background, (3) a rogue wave on a periodic wave background, (4) a rogue wave on a line soliton background and (5) a rogue wave on the two parallel solitons background. The resulting solutions are helpful for analyzing the dynamic behavior of nonlinear waves.
