This paper presents a uniform and computationally efficient analytical formulation for electromagnetic diffraction from perfectly electrically conducting (PEC) circular apertures based on the Extended Boundary Diffraction Wave (ETBDW) theory. The proposed formulation coherently incorporates incident and reflected field components within a single reflection-aware boundary-diffraction framework, thereby eliminating the field discontinuities observed in classical BDW and Kirchhoff-type models near illuminated, transition, and shadow regions. A closed-form analytical expression is derived using detour parameters and Fresnel transition functions, enabling physically continuous amplitude and phase behavior over the observation domain. The model is validated through MATLAB-based numerical evaluation of the derived closed-form ETBDW expressions and cross-checked against full-wave CST simulations for canonical PEC aperture configurations. The results show smooth field transitions near reflective edges, consistent inverse-distance decay, stable energy normalization, and agreement with reference numerical and full-wave simulation data within small deviations. Each 180° angular sweep requires less than 0.5 s in a standard MATLAB environment, confirming the suitability of the formulation for fast parametric analysis and hybrid electromagnetic solvers. The proposed model is particularly relevant for high-frequency aperture analysis, antenna modeling, radar cross-section prediction, electromagnetic shielding, and EMC-oriented simulations. To the authors’ knowledge, this work provides a closed-form uniform ETBDW formulation for reflection-aware diffraction from PEC circular apertures, combining analytical rigor with practical computational efficiency.
The classical wave kinetic equation (WKE) provides a statistical description of spectral energy transfer in weakly nonlinear dispersive systems and relies on time-translation invariance, which leads to the conventional frequency resonance condition. When the linear frequencies are periodically modulated, this symmetry is broken and an additional temporal scale is introduced, resulting in a modified resonance structure. In this work, we derive a Floquet-type wave kinetic equation for weakly nonlinear wave systems subjected to periodic frequency modulation. The resulting kinetic equation reduces to the standard WKE in the limit of vanishing modulation and provides a systematic framework for describing spectral transfer in periodically modulated wave systems. This formulation extends weak turbulence theory beyond autonomous systems by incorporating temporal modulation directly into the resonance structure of nonlinear wave interactions.
In this paper, we investigate a class of variable-coefficient generalized Lotka-Volterra binary equations with branched dispersion by employing the Hirota bilinear method to derive their bilinear representation and construct exact discrete single- and two-soliton solutions. The obtained solutions reveal that the variable coefficients play a crucial role in regulating soliton propagation, while the long-time asymptotic analysis demonstrates that two-soliton interactions remain elastic, with the solitons preserving their identities after collision except for phase shifts. Furthermore, modulation instability analysis identifies parameter regions with positive gain spectra, indicating the growth of small perturbations and providing a theoretical mechanism for the emergence of localized soliton structures. These results enrich the understanding of nonlinear wave dynamics in variable-coefficient discrete integrable systems and provide analytical insights into the effects of branched dispersion on soliton evolution.
The suppression of low-frequency duct noise presents a significant challenge in the development of ship piping systems. Recently, Sonic Black Hole (SBH) technology has garnered considerable attention due to its potential for highly efficient noise absorption. However, research on its application for duct noise control remains limited, especially in low-frequency and multi-modal control. This paper proposes a modified Quarter-Wavelength Resonator (QWR) based on the SBH paradigm, referred to as the SBH resonator. The noise attenuation characteristics and underlying mechanisms of the SBH resonator are analyzed. It is demonstrated that the proposed resonator achieves both low-frequency and multi-modal duct noise attenuation, characterized by a lower resonance frequency and a greater number of transmission loss (TL) peaks for duct noise control. To further extend the low-frequency performance, a Spiral Sonic Black Hole (SSBH) resonator is developed utilizing an Archimedean spiral profile. The SSBH resonator is demonstrated to require significantly less space while enabling effective attenuation at even lower frequencies and higher modal density. Various parameters of the SSBH resonator are analyzed. Studies identify the axial width and the truncation thickness as dominant design parameters: the former enhances the attenuation amplitude and bandwidth, while the latter provides critical tuning of the resonance frequency and bandwidth balance. Finally, experimental investigations on the noise attenuation characteristics of the SSBH resonator are conducted. The TL is measured and calculated. The accuracy and effectiveness of the current model are verified through comparison between experimental and simulation results.
Hirota’s direct method turns the construction of multisoliton solutions into algebraic identities for a bilinear symbol. For a non-polynomial dispersion law, the usual tau ansatz uses only finitely many symbol values. This gives a simple way to keep Hirota’s algebra beyond the polynomial Hirota derivatives. We use this finite-evaluation form for (DxDt+Dxp)f·f=0, where Dxp has the even multiplier |k|p and p∈C. For real p, the one-wave speed is c(k)=kp−2 for k > 0, so p controls the scale dependence of the dispersion. Complex values of p are used as an analytic continuation of this order parameter. For fixed positive wave numbers, we derive an entire cleared-denominator three-soliton obstruction Rk1,k2,k3(p) and an entire phase-shift denominator Qk1,k2,k3(p). For (k1,k2,k3)=(2,3,4), both are nontrivial: R(3)=−161280 and Q(3)=967680. We then identify the dominant exponential term for arbitrary ordered triples 0 < k1 < k2 < k3, proving that the exceptional set is discrete for every pairwise-distinct positive triple. With the order fixed, the triples that pass the cleared three-soliton condition, or have undefined phase shifts, form a real-analytic zero set of measure zero outside a discrete set of orders. Thus, except at such orders, the family has no standard arbitrary-wave-number Hirota N-soliton construction for N ≥ 3.
When potential’s wells which underlay radially symmetric traveling waves are endowed with an embedded internal hill, the spectrum of the resulting multi-modal solitary waves widens dramatically and begets an entirely new additional set of multi-modal waves. We unfold this effect within a class of compactons admitted by partial differential equations: ut+[ul−κum]x+[u∇2u]x=0, 1 < l < m, ut+[uα−κu3]x+∇2ux=0 and utt+ω2u=∇2u−uα+κu3, 0 < α < 1, all with κ=const. In the appendix, we propose an extension of this phenomenon into solitons supported by the Klein-Gordon and NLS equations.
We examine the propagation of acoustic and second-sound waves in a thermally radiating, but otherwise lossless, gas under a theory of fluids proposed by Green and Naghdi in 1995. After recalling the corresponding classical Stokes model, we first compare the two theories through Whitham-type stability criteria and show that both are stable in the parameter ranges considered. We then carry out a detailed harmonic plane-wave analysis of the Green–Naghdi model, deriving the exact dispersion relation, the associated wave branches, and amplitude ratios under boundary conditions suitable for detecting second sound. Low-frequency and small-radiation asymptotic results are obtained, revealing a branch-switching phenomenon as the ratio of acoustic to thermal-wave speed crosses unity. Finally, in the non-radiative limit, we show that the resulting dispersion relation is closely related to that arising in a monofluid description of helium II, and point out an even closer correspondence with inertial theory. These results support the view that Green–Naghdi theory provides a useful framework for second-sound propagation in radiating gases.
This paper investigates lever-type inertial amplification as a means of enhancing vibration attenuation in symmetric mono-coupled periodic structures. Using the single-cell transmissibility framework for finite arrays, an analytical model is derived for an inertial-amplified semi-cell, yielding closed-form expressions for the displacement transmissibility both with and without the rigid-bar mass contribution. The formulation predicts an induced antiresonance and a constant high-frequency asymptote, and provides explicit conditions for the existence of the antiresonance in terms of mechanism geometry and mass ratios. The inertial-amplified configuration is then compared with a baseline three-mass periodic cell, and the resulting attenuation limits are expressed in terms of tuning parameters, enabling assessment of how inertial amplification modifies attenuation bandwidth and transmissibility level for a given mass amount. Finally, two 3D-printed semi-cell prototypes are tested. The measurements reproduce the dominant predicted trends, including the emergence of the antiresonance and the tendency toward a high-frequency transmissibility plateau, while also revealing the sensitivity of the response to joint compliance, freeplay, and manufacturing asymmetry.
This article explores the integrability characteristics of the first-order generalized short-wave intermediate dispersive variable (gSIDV) equation. This equation resembles a KdV equation and possesses several intriguing attributes, including conservation properties, symmetry, and scale invariance, among others. A comprehensive integrability test is conducted, and pertinent integrability conditions are examined. The formulation of the Auto-Bäcklund transformation (ABT) through the Painlevé expansion offers a formal validation of the integrability of the gSIDV equation. By utilizing Kruskal’s simplification, a diverse range of wave structures including shock and periodic solutions are constructed from the ABT system. Additionally, auxiliary transformations are implemented to obtain direct traveling wave solutions. Finally, the application of the (G′/G)-expansion method yields a novel set of soliton solutions for the said equation. The graphical representation of the analytical forms clearly indicates that the solutions consist of solitary, shock, and periodic waves.
This paper is concerned with Pfaffian solutions of a generalized (3+1)-dimensional Jimbo-Miwa equation relevant to fluid and plasma physics. By employing the Pfaffian derivative formula under integrable parameter constraints, exact N-soliton solutions are constructed and their Pfaffian structure is analyzed. Various nonlinear wave solutions, including solitons, breathers, and interaction solutions, are generated from the obtained Pfaffian solutions. Furthermore, asymptotic analysis is performed to characterize the interaction behavior of solitons. The results provide a unified Pfaffian framework for constructing multi-soliton solutions and further illustrate the rich solution structure of the generalized Jimbo-Miwa equation.
With the rapid advancement of industry, the demand for effective noise control in complex operational environments has grown significantly, prompting increasing attention to multifunctional acoustic metamaterials. In this work, a composite neck-embedded Helmholtz resonator with a porous material liner integrated into the cavity is proposed, achieving excellent low-frequency sound absorption and enhanced thermal insulation. Theoretical and simulation results demonstrate that the incorporation of the porous material liner effectively broadens the sound absorption bandwidth, thereby enabling broadband absorption with a reduced number of absorptive units. Meanwhile, analysis indicates that a rise in temperature leads to an upward shift in the structure’s peak absorption frequency and a broadening of the bandwidth. Furthermore, a broadband absorber comprising nine such units arranged in parallel was designed and fabricated. Experimental results show an average absorption coefficient above 0.9 from 300 to 700 Hz with a deep sub-wavelength thickness of 52 mm. Additionally, measurements reveal that the incorporation of melamine foam as a porous material liner results in a 17% reduction in thermal conductivity. The proposed design thus offers dual advantages of enhanced sound absorption and thermal insulation, showing potential for engineering applications.
This paper presents a method to predict the time-domain vibro-acoustic characteristics of underwater elastic structures in a half-space environment. First, the structural dynamics equations are derived based on Hamilton's principle and thin shell theory. To accurately account for damping effects and inertial forces, the Rayleigh dissipation function is incorporated into the model. The Galerkin method is then employed for the spatial discretization of these equations, while the Precise Integration Method (PIM) is utilized to achieve an efficient and highly stable pure time-domain solution. For the acoustic domain, the time-domain equivalent source method (TD-ESM) is applied, utilizing the image source principle to accurately capture the reflection effects induced by the half-space boundaries. By establishing the fluid-structure coupling equivalence at the acoustic-structural interface, Linear Lagrange interpolation is employed to address the time-delay problem inherent in transient sound radiation. Furthermore, a regularization method is introduced to solve the ill-posed inverse problem associated with the equivalent source method, ensuring numerical stability throughout the time-domain calculation process. The proposed computational model is validated against benchmark results obtained from the FEM, demonstrating high computational accuracy, excellent numerical convergence, and strong robustness. The findings reveal that half-space boundary characteristics significantly influence the radiated sound pressure amplitude and the evolution of the time-domain waveform.
The study introduces an extended Double Legendre Orthogonal Polynomial Method (DLOPM) to investigate the influence of the inner radius, and consequently the radial wall thickness, on the vibration characteristics of piezoelectric annular Microelectromechanical Systems (MEMS) resonators with partial electrode coverage. By incorporating appropriate Legendre polynomial expansions and employing window functions to impose region-specific mechanical and electrical boundary conditions, the proposed model effectively captures wave propagation and the dissimilarities variations arising from outer-region metallization. The validity of the DLOPM is demonstrated through comparison with existing results from the literature. The study explores the dependence of resonant frequencies (RFs), antiresonant frequencies (AFs) and dynamic electromechanical coupling coefficients (DEMCCs) on the inner-to-outer radius ratio. Notably, results reveal that the DEMCC for the third mode can surpass that of the fundamental mode and increase significantly, up to a factor of 2.03, compared to equivalent solid disk configurations, particularly in thin wall thicknesses. These findings are further supported by detailed analyses of dispersion curves, frequency parameter (FP), admittance response patterns, and field distributions, providing insights into the electromechanical behavior of partially metallized annular resonators and guiding optimal device design for MEMS applications.
A variable stiffness model (VSM) of the anechoic coating is proposed to calculate the sound absorption performance under hydrostatic pressure by considering both hyperelasticity and deformation. The expression for tangent stiffness is derived based on the Mooney-Rivlin dual parameter model. A VSM algorithm is then established. For the VSM algorithm, based on the hyperelastic constitutive equation, the equivalent modulus matrix of the material and the tangent stiffness matrix of the structure are modified according to the stress and deformation state formed by hydrostatic pressure, and then applied to sound absorption calculations. The results obtained by the VSM algorithm are consistent with the experimental data reported in the literature. We find that hydrostatic pressure can cause anisotropic behavior in hyperelastic materials, and then reveal the underlying mechanisms by which hydrostatic pressure weakens the sound absorption performance of anechoic coatings in terms of geometric deformation and hyperelastic properties. This study provides a scientific basis for developing highly efficient anechoic coatings in conditions of high hydrostatic pressure, which has significant theoretical and engineering application value. It contributes to the advancement of new underwater anechoic coating technologies.
Refraction and reflection are phenomena known to occur as light travels across different media, with its speed being modulated by the refractive index. We explain how plane waves propagating at a free surface of an inviscid incompressible liquid behave in a similar manner and use a regularised wave equation, which serves as an approximation to the full water-wave equation, to show different scenarios involving constructive and destructive interference of water waves past an interface or step transition. In our case, wavespeeds are modulated by the wave frequency and the local fluid depth.
This paper aims to investigate the construction of analytical solutions for the Camassa-Holm (CH) equation. First, the Lax pair of the CH equation is rigorously derived using the prolongation structure theory, clarifying its integrability foundation. On this basis, explicit analytical solutions for single-soliton, double-soliton, and N-soliton are systematically constructed via the iterative Darboux transformation method, clearly revealing the propagation laws and elastic collision dynamics of solitons. Furthermore, the explicit form of the B & auml;cklund transformation and the superposition formula for the CH equation are derived, enabling the direct construction of rogue wave solutions and addressing the limitation of conventional methods in generating extreme wave solutions. Numerical verification results demonstrate that the obtained analytical solutions exhibit good stability and clear physical significance, effectively characterizing the dynamic behaviors of shallow water wave propagation and multiphase separation systems. This study enriches the analytical theory system of the CH equation and provides an important reference for numerical simulations and theoretical modeling in related fields such as materials science, biophysics, and fluid mechanics .
