{"title":"Investigating Rayleigh wave anisotropy in faulted media with three-component beamforming: Insights from numerical models and applications for geothermal exploration","authors":"Heather Kennedy , Claudia Finger , Katrin Löer , Amy Gilligan","doi":"10.1016/j.wavemoti.2025.103596","DOIUrl":"10.1016/j.wavemoti.2025.103596","url":null,"abstract":"<div><div>Rayleigh waves are prevalent in the ambient seismic noise wavefield and are thus often exploited in passive seismic methods to characterise the near subsurface. In fractured or faulted media, Rayleigh waves show anisotropic velocities that could provide information on the fault properties. However, the exact relationship between Rayleigh wave anisotropy and true anisotropic structures is not well known. This study used a three-component (3C) beamforming toolbox to analyse numerical full waveform seismic wave propagation from conceptual models of fractured media, which depict the nonlinear physical behaviour of the wave. We identify Rayleigh waves in the synthetic data produced from a single point source at different locations, compare observed Rayleigh wave anisotropy to structural anisotropy, and assess the effect array design and source distance have on Rayleigh wave analysis and observed anisotropy. Numerical analysis shows that the smaller the velocity contrast between fault and surrounding rock, the more complex the anisotropic response. We find that the slow directions of Rayleigh wave propagation can be a better indicator of fault strike than the fastest direction, when the velocity contrast between the two media is small.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103596"},"PeriodicalIF":2.1,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144510979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Propagation of acoustic solitons in a nonlinear left-handed transmission line","authors":"Dahirou Mahmoud , Saïdou Abdoulkary , L.Q. English , Alidou Mohamadou","doi":"10.1016/j.wavemoti.2025.103597","DOIUrl":"10.1016/j.wavemoti.2025.103597","url":null,"abstract":"<div><div>We study analytically and numerically acoustic soliton propagation in a nonlinear left-handed transmission line with nonlinear elements that incorporate Helmholtz resonators. We propose a theoretical model of the system integrating acoustic compliance with nonlinear effects, which relies on a transmission-line approach. Importantly, by means of a semi-discrete approximation, we can derive a nonlinear Schrödinger equation and thus show that the system supports both bright and dark acoustic solitons depending on the choice of carrier frequency. The values of the Helmholtz resonators parameters strongly influence the frequency bands, the stability of the waves, as well as their propagation. We perform systematic numerical simulations of the Nonlinear Schrödinger equation (NLSE) to show the spectral stability/instability of the initial waves. We then demonstrate that the nonlinear discrete lattice model can support the propagation of the solitons borrowed from the NLSE. Our findings suggest that the predicted structures are quite robust and the acoustic solitons persists throughout long simulation times.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103597"},"PeriodicalIF":2.1,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144513854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"PT symmetry preserving, symmetry breaking and propagation behaviors in degenerate and non-degenerate solitons beyond the nonlocal Manakov system","authors":"Yang-Yang Du , Yan-Nan Zhao , Rui Guo , Jian-Wen Zhang","doi":"10.1016/j.wavemoti.2025.103593","DOIUrl":"10.1016/j.wavemoti.2025.103593","url":null,"abstract":"<div><div>It is known that the four-wave mixing (FWM) not only serves as the basic paradigm for optical signal processing but can also result in the generation of more complex wave phenomena. In this paper, we investigate the properties of non-degenerate and degenerate solitons and their relevant collision dynamics for the generalized nonlocal Manakov system, which contains the FWM term. To start with, non-degenerate one-soliton solutions are derived by the Hirota’s bilinear method, and degenerate one- and two-soliton solutions (under specific restrictions on wave numbers) are also obtained in this way. Then, we illustrate the implications of the FWM for the humps of non-degenerate solitons briefly. To learn about the features of the nonlocalization, we obtain <span><math><mrow><mi>P</mi><mi>T</mi></mrow></math></span> symmetry preserving and symmetry breaking soliton solutions, and identify stable and unstable propagations of soliton evolution for different modes. Given that the propagations of the mixed modes are stable, we investigate two discrepant types of collisions for degenerate two-soliton solutions, which are shown not to be conserved in energy for the individual solitons after the asymptotic analyses are constructed. This energy non-conservation characteristic of the collisions is in contrast to the nonlocal Manakov system, which is attributed to the FWM. Finally, taking into account the particularity of wave velocity, we also present the localized resonant pattern for different collisions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103593"},"PeriodicalIF":2.1,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-24DOI: 10.1016/j.wavemoti.2025.103592
Xue-Hui Zhao , Guo-Hong Yang , Zhong-Zhou Lan
{"title":"Dynamics and interactions of bound-state Solitons for a coupled Hirota system with negative coherent coupling","authors":"Xue-Hui Zhao , Guo-Hong Yang , Zhong-Zhou Lan","doi":"10.1016/j.wavemoti.2025.103592","DOIUrl":"10.1016/j.wavemoti.2025.103592","url":null,"abstract":"<div><div>In this paper, We investigate the dynamics and interactions of bound-state solitons in a coupled Hirota system with negative coherent coupling. Using the <span><math><mi>N</mi></math></span>th-order binary Darboux transformation, we derive <span><math><mi>N</mi></math></span>-soliton solutions and analyze four distinct cases of bound-state soliton dynamics through spectral parameter constraints. Our results demonstrate how the higher-order perturbation parameter <span><math><mi>ɛ</mi></math></span> modulates nonlinear coupling, governing transitions between fusion, fission, and mixed interaction states. These findings provide new insights into soliton manipulation in nonlinear optical media and complex coupled systems, with potential applications in optical communications and signal processing.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103592"},"PeriodicalIF":2.1,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144480101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-23DOI: 10.1016/j.wavemoti.2025.103601
Majdi O. Gzal , Lawrence A. Bergman , Kathryn H. Matlack , Alexander F. Vakakis
{"title":"Low-frequency sub-Bragg phenomena in multilayered vibroacoustic metamaterials","authors":"Majdi O. Gzal , Lawrence A. Bergman , Kathryn H. Matlack , Alexander F. Vakakis","doi":"10.1016/j.wavemoti.2025.103601","DOIUrl":"10.1016/j.wavemoti.2025.103601","url":null,"abstract":"<div><div>Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve broadband low-frequency sound manipulation at the sub-wavelength scale in a multilayered vibroacoustic metamaterial. Remarkably, we unveil the formation of genuinely sub-wavelength Bragg-like band-splitting induced bandgaps, generalizing the \"band-folding induced bandgaps\" in the literature. Additionally, we propose a methodology to widen sub-wavelength local resonance bandgaps by hosting two local resonances within the same bandgap. These sub-Bragg phenomena are realized at low frequencies in an axisymmetric vibroacoustic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The coupled sound-structure interaction is solved exactly. The studied system exhibits sub-wavelength acoustical transparency, akin to “electromagnetically induced transparency”, and an acoustic analogue of \"plasma oscillations\". We derive canonical conditions for the emergence of band-splitting bandgaps, showing they are exclusive to multilayered configurations. These band-splitting bandgaps resemble Bragg bandgaps in their attenuation, band-crossing capabilities, and potential to host topological interface states. We also reveal that classical geometric Bragg diffraction does not apply to the periodic multilayered vibroacoustic configurations examined. The studied sub-wavelength phenomena unlock new possibilities for controlling low-frequency wave propagation in the sub-Bragg regime. Design guidelines for maximizing bandgap width within the low-frequency regime are provided, and the attenuation performance across different bandgaps is demonstrated through numerical simulations. We anticipate that our findings, while demonstrated here in vibroacoustic metamaterials, provide a promising approach for advanced acoustic devices, and could inspire future work exploring similar sub-wavelength mechanisms in other classes of physical systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103601"},"PeriodicalIF":2.1,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-22DOI: 10.1016/j.wavemoti.2025.103595
Philip G. Kaufinger , John M. Cormack , Kyle S. Spratt , Mark F. Hamilton
{"title":"Perturbation solution for second-harmonic generation in focused shear wave beams in soft solids","authors":"Philip G. Kaufinger , John M. Cormack , Kyle S. Spratt , Mark F. Hamilton","doi":"10.1016/j.wavemoti.2025.103595","DOIUrl":"10.1016/j.wavemoti.2025.103595","url":null,"abstract":"<div><div>Plane nonlinear shear waves in isotropic media are subject only to cubic nonlinearity at leading order and therefore generate only odd harmonics during propagation. Wavefront curvature in shear wave beams breaks the symmetry in the material response and yields quadratic nonlinearity, such that a second harmonic may be generated at second order in a shear wave beam depending on the polarization of the wave field. The governing paraxial wave equation accounting for both quadratic and cubic nonlinearity in isotropic elastic media was derived originally by Zabolotskaya (1986), with its formulation employed in the present work developed subsequently by Wochner et al. (2008). Closed-form analytical solutions for the fields at the source frequency and the second harmonic are derived by perturbation for both the transverse and longitudinal particle displacement components in focused shear wave beams radiated by a source defined by affine polarization, Gaussian amplitude shading, and quadratic phase shading to account for focusing. Examples of field distributions are presented based on parameters reported by Cormack et al. (2024) for measurements of radially polarized focused shear wave beams generated in tissue-mimicking phantoms. Second-harmonic generation in shear wave beams with other polarizations is also discussed. Calculations are presented to estimate the vibration amplitude required for observable second-harmonic generation in tissue-mimicking phantoms. It is postulated that the second harmonic may be used to estimate the third-order elastic material property as an additional biomarker for diseased tissue.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103595"},"PeriodicalIF":2.1,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-21DOI: 10.1016/j.wavemoti.2025.103598
Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu
{"title":"Analytical and numerical investigations of the interaction between nonlinear guided wave mixing and micro-cracks in pipe-like structures","authors":"Maoxun Sun , Miaohong Tan , Cheng Shan , Yue Zhang , Hongye Liu","doi":"10.1016/j.wavemoti.2025.103598","DOIUrl":"10.1016/j.wavemoti.2025.103598","url":null,"abstract":"<div><div>Underground or underwater pipe-like structures are usually subjected to corrosion or plastic deformation, during which the micro-cracks probably appear and gradually evolve into macro-cracks, resulting in the leakage of pipes. Therefore, to avoid catastrophic accidents, it is necessary to locate micro-cracks accurately and repair or replace pipes in time. Wave mixing has the advantages of micro-crack localization compared with second harmonics, and it can avoid the interference of nonlinearities in measurement systems. However, few reports are available on nonlinear mixing of counter-propagating guided waves caused by contact acoustic nonlinearity (CAN) in pipes. In this paper, the interaction of the guided wave mixing and micro-cracks in pipe-like structures is theoretically and numerically investigated via CAN and vector analyses, as well as pulse-inversion techniques and two-dimensional fast Fourier transforms (2D-FFT), respectively. It is theoretically demonstrated that the amplitudes of second-order harmonics increase monotonically with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>, while the amplitudes of third-order harmonics first increase and then drop with <em>ε</em><sub>0</sub>/<em>ε</em><sup>0</sup>. In simulations, nonlinear mixing of counter-propagating guided waves occurs in the regions that contain micro-cracks, and the generated difference-frequency components or sum-frequency components propagate to both ends of pipes at the same time. The difference-frequency components mainly contain F(<em>m</em>,1) modes, and the sum-frequency components mainly contain F(<em>m</em>,2) modes and F(<em>m</em>,3) modes, which are predicted in advance by theoretical investigations. In addition, the normalized amplitudes of difference-frequency components and sum-frequency components exhibit “mountain-shape” trends between 0° and 90° as well as during 90° and 180°, with the peaks corresponding to micro-crack angles of 45° and 135° Note that they reach the minimums when angles of micro-cracks equal to 0°, 90° or 180°, which is in a good agreement with the theoretical investigations. Finally, the <em>z</em>-coordinates of micro-cracks can be determined by the relationship between the normalized amplitudes of difference-frequency components or sum-frequency components and positions of mixing zones. The <em>φ</em>-coordinates of micro-cracks can be obtained based on normalized amplitudes of difference-frequency components in U<em><sub>z</sub></em> with respect to <em>φ</em>-coordinates.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103598"},"PeriodicalIF":2.1,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-20DOI: 10.1016/j.wavemoti.2025.103599
Tianshu Liang, Ying Liu, Qingxiao Gu
{"title":"Opto-band tuning in a liquid crystal elastomer phononic crystal plate","authors":"Tianshu Liang, Ying Liu, Qingxiao Gu","doi":"10.1016/j.wavemoti.2025.103599","DOIUrl":"10.1016/j.wavemoti.2025.103599","url":null,"abstract":"<div><div>Based on the light sensitivity of liquid crystal elastomers, a Grille-like phononic crystal plate is proposed in this paper with the aim to achieve multi-mode band opto-tuning. The indirect coupling strategy is used to determine the opto-band variation in phononic crystal plate. The spontaneous deformation of the phononic crystal plate is firstly investigated. Then the wave dispersion in the opto-deformed phononic crystal plate is explored. The band structure in undeformed phononic crystal plate is also given for comparison. The effects of geometrical sizes of unit cells and light intensity are clarified in detail. The result indicates that the band structures in phononic crystal plates can be tuned by adjusting the light intensity, which displays sensitive dependence on the unit cell geometrical sizes. The phononic crystal plate with opto-deformable slabs provides a choice in design of opto-controlling phononic crystal plate, and has prospective applications in optical controlling of devices and systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103599"},"PeriodicalIF":2.1,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-18DOI: 10.1016/j.wavemoti.2025.103561
R. Abouem A. Ribama , Z.I. Djoufack , J.P. Nguenang
{"title":"Influence of the mass ratio on the formation of gap intrinsic localized structures and energy distribution in a 1D Frenkel–Kontorova quantum diatomic chain","authors":"R. Abouem A. Ribama , Z.I. Djoufack , J.P. Nguenang","doi":"10.1016/j.wavemoti.2025.103561","DOIUrl":"10.1016/j.wavemoti.2025.103561","url":null,"abstract":"<div><div>We investigate the mass ratio influence on the formation of gap intrinsic localized structures and energy distribution in a 1D Frenkel–Kontorova quantum diatomic chain. We analyze the coupled nonlinear excitations and it is found that : On the one hand, a gap frequency is obtained through the linear spectrum as well as different families of gap breather solutions depending on the gap frequency values, On the other hand, the existence of intrinsic localized structures for some particular frequencies in the vicinity of the gap and the formation of the modulation instability (MI) zones, as well as the intensity of the growth rate in addition to the amplitude of energy density can be influenced by the mass ratio of particles. Furthermore, there is a large gap opened in the phonon spectrum for a very small mass ratio and the phenomenon of gap cannot exist if the above condition is not satisfied. The accuracy of the analytical studies is confirmed by an excellent agreement with the numerical simulations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103561"},"PeriodicalIF":2.1,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144330160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wave MotionPub Date : 2025-06-11DOI: 10.1016/j.wavemoti.2025.103584
Majid Madadi , Mustafa Inc , Mustafa Bayram
{"title":"Nonlinear wave behaviors for a combined Kadomtsev–Petviashvili–Boiti–Leon–Manna–Pempinelli equation in fluid dynamics, plasma physics and nonlinear optics","authors":"Majid Madadi , Mustafa Inc , Mustafa Bayram","doi":"10.1016/j.wavemoti.2025.103584","DOIUrl":"10.1016/j.wavemoti.2025.103584","url":null,"abstract":"<div><div>Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores a newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev–Petviashvili (KPE) and Boiti–Leon–Manna–Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that it does not satisfy the Painlevé property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103584"},"PeriodicalIF":2.1,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}