Wave Motion最新文献

{"title":"On the matrix negative order Korteweg–de Vries equation — the commutative case","authors":"T. Kriecherbauer ,&nbsp;G.U. Urazboev ,&nbsp;A.K. Babadjanova","doi":"10.1016/j.wavemoti.2025.103562","DOIUrl":"10.1016/j.wavemoti.2025.103562","url":null,"abstract":"<div><div>This work is devoted to the application of the inverse scattering transform method to the matrix negative order Korteweg–de Vries (mNKdV) equation in the commutative case. First, we obtain the time evolution of the scattering data for the corresponding matrix Sturm–Liouville operator with a self-adjoint potential. This then leads to a general construction procedure for solutions of the mNKdV equation that can also be used for solving initial value problems. We illustrate our results by presenting explicit formulas for arbitrary multi-soliton solutions in the reflectionless case.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103562"},"PeriodicalIF":2.1,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899334","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":"Well-posed boundary conditions and energy stable discontinuous Galerkin spectral element method for the linearized Serre equations","authors":"Kenny Wiratama ,&nbsp;Kenneth Duru ,&nbsp;Stephen Roberts ,&nbsp;Christopher Zoppou","doi":"10.1016/j.wavemoti.2025.103564","DOIUrl":"10.1016/j.wavemoti.2025.103564","url":null,"abstract":"<div><div>We derive a class of well-posed boundary conditions for the linearized Serre equations in one spatial dimension using the energy method. The boundary conditions are formulated such that they are amenable to high order numerical methods. The resulting initial boundary value problem (IBVP) is energy stable, facilitating the design of robust and arbitrarily accurate numerical methods. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind numerical fluxes is proposed for solving the IBVP. For the numerical approximation, we derive discrete energy estimates by mimicking the continuous energy estimates and provide a priori error estimates in the energy norm. Detailed numerical examples are presented to verify the theoretical analysis and demonstrate convergence of numerical errors.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103564"},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895879","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":"Control of Bleustein-Gulyaev (BG) waves by a locally resonant meta-surface","authors":"Yu Pang ,&nbsp;Qiyuan Duan ,&nbsp;Wenjie Feng ,&nbsp;Xuan Zhao","doi":"10.1016/j.wavemoti.2025.103575","DOIUrl":"10.1016/j.wavemoti.2025.103575","url":null,"abstract":"<div><div>A locally resonant meta-surface can manipulate surface wave propagation. In this paper, we investigate the propagation of Bleustein-Gulyaev (BG) waves in a piezoelectric (PE) half space coupled to a locally resonant meta-surface. The meta-surface consists of an array of sub-wavelength spring-mass resonators attached to the free surface of a PE half-space. Using the effective medium approximation, we analytically obtain an explicit dispersion equation of BG wave on the meta-surface. A finite element model (FEM) is proposed to validate the analytical method. The propagating BG wave hybridizing with the surface resonance excites a guided mode and the electromechanical coupling properties of BG wave result in a higher mode, which are below and above the resonance frequency, respectively. An avoided crossing band gap occurs due to the local resonance. Within the band gap, BG wave transforms into shear bulk wave. The band gap and wave mode shapes are tunable non-destructively via the interaction parameters. By enhancing this interaction, the band gap becomes wider while the displacements, electric potentials and stresses at lower frequencies decay more slowly than those at higher frequencies. In addition, a stronger electric field is excited by the local resonance coupled with the PE half-space. The present work proposes a simply way to manipulate surface acoustic wave (SAW) without any change on geometrical or material properties of original host substrate. Hence, this way is low-cost and convenient. Besides, the model of spring-mass resonators is instructive for a better understanding the general behavior of wave-guiding by local resonance. It is expected that the current model will be applied in practice to design SH wave-based SAW filters and resonators.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103575"},"PeriodicalIF":2.1,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899335","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":"Persistence of integrable wave dynamics in the Discrete Gross–Pitaevskii equation: The focusing case","authors":"G. Fotopoulos ,&nbsp;N.I. Karachalios ,&nbsp;V. Koukouloyannis","doi":"10.1016/j.wavemoti.2025.103560","DOIUrl":"10.1016/j.wavemoti.2025.103560","url":null,"abstract":"<div><div>Expanding upon our prior findings on the proximity of dynamics between integrable and non-integrable systems within the framework of nonlinear Schrödinger equations, we examine this phenomenon for the focusing Discrete Gross–Pitaevskii equation in comparison to the Ablowitz–Ladik lattice. The presence of the harmonic trap necessitates the study of the Ablowitz–Ladik lattice in weighted spaces. We establish estimates for the distance between solutions in the suitable metric, providing a comprehensive description of the potential evolution of this distance for general initial data. These results apply to a broad class of nonlinear Schrödinger models, including both discrete and partial differential equations. For the Discrete Gross–Pitaevskii equation, they guarantee the long-term persistence of small-amplitude bright solitons, driven by the analytical solution of the AL lattice, especially in the presence of a weak harmonic trap. Numerical simulations confirm the theoretical predictions about the proximity of dynamics between the systems over long times. They also reveal that the soliton exhibits remarkable robustness, even as the effects of the weak harmonic trap become increasingly significant, leading to the soliton’s curved orbit.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103560"},"PeriodicalIF":2.1,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878871","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":"New exact solutions of the (3+1)-dimensional defocusing Gardner–KP equation using Lie symmetry analysis","authors":"Yongxin Liu,&nbsp;Jinyu Wu,&nbsp;Xuelin Yong","doi":"10.1016/j.wavemoti.2025.103559","DOIUrl":"10.1016/j.wavemoti.2025.103559","url":null,"abstract":"<div><div>In this paper, an attempt is made to present the rigorous and comprehensive group analysis of the (3+1)-dimensional defocusing Gardner–KP equation. According to the Lie invariance condition, the Lie algebra of infinitesimal symmetries spanned by eight vector fields is found. The commutator and adjoint representation tables are derived, and a detailed process for searching the optimal system of one-dimensional subalgebras is shown. Several symmetry reductions and group-invariant solutions with physical or mathematical interests are obtained by using infinitesimal generators in the optimal system. Some new particular solutions are deduced by using effective invariant-solution ansatz and the solutions of a second-order elliptic equation with power-law nonlinearity. Especially, by recasting the reduced two-dimensional counterpart equation into Hirota’s bilinear form, the fundamental solitary waves are found. And a special kind of flat-top soliton excitation is exhibited. It is also shown that this (3+1)-dimensional equation can have only unidirectional multiple-soliton solutions and does not allow soliton resonance to occur. The physical interpretations of resulting solutions are illustrated by three-dimensional graphics through numerical simulation. Different types of two-soliton interactions are also demonstrated in graphical ways.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103559"},"PeriodicalIF":2.1,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143867811","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":"Novel soliton motion with time-varying wave-width and amplitude as well as velocity through a reverse-space-time nonlocal variable-coefficient mKdV equation","authors":"Xianghui Wang,&nbsp;Sheng Zhang","doi":"10.1016/j.wavemoti.2025.103558","DOIUrl":"10.1016/j.wavemoti.2025.103558","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Nonlocal integrable systems have received widespread attention because of their special physical effects. In this article, we present a novel reverse-space-time nonlocal variable-coefficient mKdV (RSTVmKdV) equation and reveal its &lt;em&gt;N&lt;/em&gt;-soliton solution by Riemann–Hilbert (RH) method. We notice that the revealed soliton solutions are tilted and exhibit the following behavioral characteristics: their wave width, amplitude, and velocity vary over time. This is novel for the isospectral soliton equation. In terms of specific content, firstly, we give the Lax pair of a system of coupled mKdV equations with time-varying coefficients and construct the related solvable RH problem. Then, we analyze the symmetry of eigenvalues &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Finally, we derive the general formula for the &lt;em&gt;N&lt;/em&gt;-soliton solution and the specific expression for single soliton solution of the RSTVmKdV equation. Through mathematical analysis and simulation, we find that when the related eigenvalues &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mover&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; are not conjugate, the single-soliton solution depicted is not symmetric, and when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mover&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the soliton tilts towards the negative &lt;em&gt;x&lt;/em&gt;-axis, while when &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mover&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, the soliton tilts towards the positive &lt;em&gt;x&lt;/em&gt;-axis. In addition, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; affect the amplitude of solitons in the case of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;msub&gt;&lt;mover&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mover&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, while &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; affect the wave width, speed, and propagation direction of solitons. The results indicate that the method proposed in this paper can be used to derive and solve other reverse-space-time nonlocal integrable systems with time-varying coefficients and explore their rich soliton behavior.&lt;/div&gt;&lt;/di","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"137 ","pages":"Article 103558"},"PeriodicalIF":2.1,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815989","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":"Study of lamb wave hybrid imaging technology in high noise environments","authors":"Yun Chen ,&nbsp;Gaoping Wang ,&nbsp;Zhiyuan Li","doi":"10.1016/j.wavemoti.2025.103548","DOIUrl":"10.1016/j.wavemoti.2025.103548","url":null,"abstract":"<div><div>Ultrasonic Lamb waves often face challenges in extracting valid signals due to environmental noise when detecting damage in composite materials. Additionally, the presence of excessive invalid data can significantly reduce detection efficiency. To solve this issue, a hybrid damage detection method, based on box-counting dimensions and optimized path probabilistic imaging (OPPIBCD), is proposed for use in noisy environments. A damage detection platform is established, with sensors evenly arranged in a circular grid on a composite material plate to simulate real damage through bonded mass blocks. Experimental results indicate that, in high-noise environments, the detection efficiency for single and multiple damage imaging paths improves by 80 % and 65 %, respectively, with maximum errors of 8 mm and 11 mm. The proposed method does not require signal denoising techniques and can directly use the collected noisy signals for damage detection, achieving both high efficiency and accuracy.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"138 ","pages":"Article 103548"},"PeriodicalIF":2.1,"publicationDate":"2025-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143834872","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":"Surface disturbances of fluid due to vertical surface-piercing cylinder","authors":"Martin Kocan ,&nbsp;Douglas A. Potts ,&nbsp;Jonathan R. Binns ,&nbsp;Alexei T. Skvortsov","doi":"10.1016/j.wavemoti.2025.103550","DOIUrl":"10.1016/j.wavemoti.2025.103550","url":null,"abstract":"<div><div>Studying the profile of fluid surfaces caused by a vertical surface-piercing cylinder has a long history. First results date back to the seminal work of Lord Kelvin. This problem still presents a challenge for analytical treatment and requires advanced computational tools and sophisticated experimental facilities. Our study proposes a simplified physics-based model for the estimation of the bow wave run-up on the front of a vertical surface-piercing cylinder and the calculation of gravity–capillary waves in steady flows at high Froude numbers. The model assumes conservation of momentum of the surface-piercing cylinder being transferred to the free surface of the fluid and the effects of gravity, capillarity and viscosity for the computation of the fluid motion around the cylinder. The model is validated against experiments performed in a towing tank for different cylinder diameters and results from previous studies.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"137 ","pages":"Article 103550"},"PeriodicalIF":2.1,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821242","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":"Rogue waves of the Kraenkel–Manna–Merle system on a periodic background","authors":"Chun Chang,&nbsp;Zhaqilao","doi":"10.1016/j.wavemoti.2025.103545","DOIUrl":"10.1016/j.wavemoti.2025.103545","url":null,"abstract":"<div><div>In this paper, we summarize the construction of rogue wave solutions for the Kraenkel–Manna–Merle system on the background of Jacobian elliptic dn- and cn-periodic waves. Our approach involved nonlinearizing the Lax pair to derive eigenvalues and eigenfunctions, introducing periodic and non-periodic solutions of the Lax pair, and utilizing the Darboux transformation to establish potential relations. Consequently, we obtain periodic rogue wave solutions and conducted a nonlinear dynamics analysis, revealing significant insights into the behavior of the Kraenkel–Manna–Merle system. A rogue wave on a skewed periodic wave background is obtained which is a novel phenomenon in the nonlinear system.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"137 ","pages":"Article 103545"},"PeriodicalIF":2.1,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760967","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":"Fourth-order Stokes theory for capillary–gravity waves in arbitrary water depth on linear shear currents","authors":"Suman Mukherjee,&nbsp;Sourav Halder,&nbsp;A.K. Dhar","doi":"10.1016/j.wavemoti.2025.103546","DOIUrl":"10.1016/j.wavemoti.2025.103546","url":null,"abstract":"<div><div>In this paper the two-dimensional steady surface capillary–gravity waves, incorporating the effects of linear shear currents, is studied in water of constant depth. Herein, linear shear currents are considered to be a linear combination of depth-uniform current and uniform vorticity. Employing an excellent Stokes expansion method, where the expansion parameter represents the wave steepness itself, a fourth-order perturbation series solution for plane progressive waves is developed. The key results of this work are (a) to find the influence of both co-flowing and counter-flowing currents on the wave profiles using the fourth-order approximation (b) the strong dependence of the wave velocity on both the magnitudes of the shear and depth-uniform current, (c) the Wilton singularities in the Stokes expansion in powers of wave amplitude due to a inverse Bond number of <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></math></span> and <span><math><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></math></span>, which are the results of the non-uniformity in the ordering of the Fourier coefficients are observed to be influenced by vorticity and depth-uniform current, (d) distinct surface profiles of capillary–gravity waves are obtained and the effects of depth-uniform currents on these profiles are described. This analysis also shows that for any given value of the water depth, there exist a threshold value of the vorticity above which no resonances occur. For the steepest waves considered in this analysis, it is observed that when the wavenumber is not in the vicinity of certain critical values, determined by the depth and the vorticity, the present fourth-order analysis shows significant deviations on the surface profiles from the third-order analysis and provides better results consistent with the exact numerical results.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"137 ","pages":"Article 103546"},"PeriodicalIF":2.1,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143747353","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}