Pub Date : 2024-11-19DOI: 10.1016/j.wavemoti.2024.103448
Jiaqing Shan, Maohua Li
In this paper, by using the Darboux transformation (DT), two types of breather solutions for the reverse space–time (RST) nonlocal short pulse equation are constructed in nonzero background: bounded and unbounded breather solutions. The degenerate DT is obtained by taking the limit of eigenvalues and performing a higher-order Taylor expansion. Then the order breather-positon solutions are generated through degenerate DT. Some properties of the breather-positon solutions are discussed. Furthermore, rogue wave solutions are derived through the degeneration of breather-positon solutions.
{"title":"The breather, breather-positon, rogue wave for the reverse space–time nonlocal short pulse equation in nonzero background","authors":"Jiaqing Shan, Maohua Li","doi":"10.1016/j.wavemoti.2024.103448","DOIUrl":"10.1016/j.wavemoti.2024.103448","url":null,"abstract":"<div><div>In this paper, by using the Darboux transformation (DT), two types of breather solutions for the reverse space–time (RST) nonlocal short pulse equation are constructed in nonzero background: bounded and unbounded breather solutions. The degenerate DT is obtained by taking the limit of eigenvalues and performing a higher-order Taylor expansion. Then the <span><math><mi>N</mi></math></span> order breather-positon solutions are generated through degenerate DT. Some properties of the breather-positon solutions are discussed. Furthermore, rogue wave solutions are derived through the degeneration of breather-positon solutions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103448"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747047","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}
Pub Date : 2024-11-19DOI: 10.1016/j.wavemoti.2024.103446
L.M.B.C. Campos, M.J.S. Silva
The energy balance equation, including not only the kinetic and deformation energy densities, but also the power of external forces, identifies the energy flux as minus the product of the velocity by the stress tensor: this result does not depend on constitutive relations and applies to elastic or inelastic matter. The simplest case is an isotropic pressure, when the energy flux equals its product by the velocity. In the linear case, the energy flux is obtained in elasticity for crystals and amorphous matter. An independent result is to show that, by inspection of any linear wave equation in a steady homogeneous medium, it is possible to ascertain whether the waves are (a) isotropic or not and (b) dispersive or not, with no need for an explicit solution. An application of this result to linear elastic waves shows that: (i) they are non-dispersive in crystals or amorphous matter; (ii) for the latter material, the longitudinal and transversal waves are isotropic, but their sum is not. A consequence of (ii) is that the superposition of longitudinal and transversal waves: () adds the two energy densities and powers of external forces; () adds, to the two energy fluxes, a third cross-coupling energy flux that is proportional to the dilatation of the longitudinal wave multiplied by the velocity of the transverse wave.
{"title":"On the energy flux in elastic and inelastic bodies and cross-coupling flux between longitudinal and transversal elastic waves","authors":"L.M.B.C. Campos, M.J.S. Silva","doi":"10.1016/j.wavemoti.2024.103446","DOIUrl":"10.1016/j.wavemoti.2024.103446","url":null,"abstract":"<div><div>The energy balance equation, including not only the kinetic and deformation energy densities, but also the power of external forces, identifies the energy flux as minus the product of the velocity by the stress tensor: this result does not depend on constitutive relations and applies to elastic or inelastic matter. The simplest case is an isotropic pressure, when the energy flux equals its product by the velocity. In the linear case, the energy flux is obtained in elasticity for crystals and amorphous matter. An independent result is to show that, by inspection of any linear wave equation in a steady homogeneous medium, it is possible to ascertain whether the waves are (a) isotropic or not and (b) dispersive or not, with no need for an explicit solution. An application of this result to linear elastic waves shows that: (i) they are non-dispersive in crystals or amorphous matter; (ii) for the latter material, the longitudinal and transversal waves are isotropic, but their sum is not. A consequence of (ii) is that the superposition of longitudinal and transversal waves: (<span><math><mi>α</mi></math></span>) adds the two energy densities and powers of external forces; (<span><math><mi>β</mi></math></span>) adds, to the two energy fluxes, a third cross-coupling energy flux that is proportional to the dilatation of the longitudinal wave multiplied by the velocity of the transverse wave.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103446"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747048","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}
Pub Date : 2024-11-19DOI: 10.1016/j.wavemoti.2024.103447
Arnaud Recoquillay
This paper presents the use of phased array data as the input of the Linear Sampling Method for elastic waveguides. Indeed, this method enables the high frequency, hence high resolution, inspection of waveguides, which is of interest for example for nondestructive testing applications. However, the use of single emitter data, also known as Full Matrix Capture in the Non Destructive Testing (NDT) context, leads to poor signal to noise ratios as low amplitude signals are emitted and only a fraction of the energy reaches the potential defect. The use of phase laws, that is the simultaneous emission with multiple sensors, enables better signal to noise ratios. However, the drawback may be a loss on the conditioning of the method, which may lead to higher sensitivity to noise in the end. This paper shows how to choose the sensors and the phase laws to obtain a satisfactory imaging results. This is exemplified on experimental data acquired in a steel plate with a circular hole.
{"title":"On the use of phase laws for the Linear Sampling Method in an elastic waveguide. Application to nondestructive testing","authors":"Arnaud Recoquillay","doi":"10.1016/j.wavemoti.2024.103447","DOIUrl":"10.1016/j.wavemoti.2024.103447","url":null,"abstract":"<div><div>This paper presents the use of phased array data as the input of the Linear Sampling Method for elastic waveguides. Indeed, this method enables the high frequency, hence high resolution, inspection of waveguides, which is of interest for example for nondestructive testing applications. However, the use of single emitter data, also known as Full Matrix Capture in the Non Destructive Testing (NDT) context, leads to poor signal to noise ratios as low amplitude signals are emitted and only a fraction of the energy reaches the potential defect. The use of phase laws, that is the simultaneous emission with multiple sensors, enables better signal to noise ratios. However, the drawback may be a loss on the conditioning of the method, which may lead to higher sensitivity to noise in the end. This paper shows how to choose the sensors and the phase laws to obtain a satisfactory imaging results. This is exemplified on experimental data acquired in a steel plate with a circular hole.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103447"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747045","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}
Pub Date : 2024-11-19DOI: 10.1016/j.wavemoti.2024.103445
Ameer B. Batarseh , M. Javad Zakeri , Andrea Blanco-Redondo , Marek Trippenbach , David Hagan , Wieslaw Krolikowski , Pawel S. Jung
Bright solitons with two in-phase peaks can form in a nonlinear homogeneous medium due to competing nonlocal interactions. This study explores the emergence and transformation of these solitons, considering both additive and multiplicative models for the competing nonlinear self-focusing and self-defocusing effects. We show that high input power can trigger the formation of the stable, double-peaked solitons. Furthermore, we introduce a semi-analytical approach (SAA) to accurately predict the critical conditions where single-peak solitons transition to double-peak ones. The SAA combines the variational approach with a linear eigenmode solver, achieving good agreement with exact simulations while being significantly faster. Our work emphasizes the importance of nonlocality in soliton formation and introduces SAA as a valuable tool for future investigations.
{"title":"Crossover from single to two-peak fundamental solitons in nonlocal nonlinear media","authors":"Ameer B. Batarseh , M. Javad Zakeri , Andrea Blanco-Redondo , Marek Trippenbach , David Hagan , Wieslaw Krolikowski , Pawel S. Jung","doi":"10.1016/j.wavemoti.2024.103445","DOIUrl":"10.1016/j.wavemoti.2024.103445","url":null,"abstract":"<div><div>Bright solitons with two in-phase peaks can form in a nonlinear homogeneous medium due to competing nonlocal interactions. This study explores the emergence and transformation of these solitons, considering both additive and multiplicative models for the competing nonlinear self-focusing and self-defocusing effects. We show that high input power can trigger the formation of the stable, double-peaked solitons. Furthermore, we introduce a semi-analytical approach (SAA) to accurately predict the critical conditions where single-peak solitons transition to double-peak ones. The SAA combines the variational approach with a linear eigenmode solver, achieving good agreement with exact simulations while being significantly faster. Our work emphasizes the importance of nonlocality in soliton formation and introduces SAA as a valuable tool for future investigations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103445"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747051","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}
Pub Date : 2024-11-19DOI: 10.1016/j.wavemoti.2024.103449
Pengcheng Xin, Zhonglong Zhao, Yu Wang
The Fokas system is widely applied in nonlinear optics which can be used to describe the propagation behavior of optical solitons. An effective method for constructing the quasi-periodic breathers of the Fokas system is presented by combining the Hirota’s bilinear method with the theta function. The solvable problem of the quasi-periodic breathers is successfully transformed into a least squares problem whose numerical solutions ultimately are obtained through the Gauss–Newton method and the Levenberg–Marquardt method. Theoretical inference and numerical results show that when the real part of the diagonal elements of the Riemann matrix tends to positive infinity, the quasi-periodic breathers can be reduced to regular breathers. By analyzing the propagation characteristics of the quasi-periodic breathers, these quasi-periodic breathers are divided into three categories, general quasi-periodic breathers, quasi-periodic approximate Kuznetsov–Ma breathers and quasi-periodic Akhmediev breathers. Furthermore, by using an analytical method related to the characteristic lines for the quasi-periodic breathers, the dynamic characteristics including the periods and wave velocities of the quasi-periodic breathers are analyzed.
{"title":"Quasi-periodic breathers and their dynamics to the Fokas system in nonlinear optics","authors":"Pengcheng Xin, Zhonglong Zhao, Yu Wang","doi":"10.1016/j.wavemoti.2024.103449","DOIUrl":"10.1016/j.wavemoti.2024.103449","url":null,"abstract":"<div><div>The Fokas system is widely applied in nonlinear optics which can be used to describe the propagation behavior of optical solitons. An effective method for constructing the quasi-periodic breathers of the Fokas system is presented by combining the Hirota’s bilinear method with the theta function. The solvable problem of the quasi-periodic breathers is successfully transformed into a least squares problem whose numerical solutions ultimately are obtained through the Gauss–Newton method and the Levenberg–Marquardt method. Theoretical inference and numerical results show that when the real part of the diagonal elements of the Riemann matrix tends to positive infinity, the quasi-periodic breathers can be reduced to regular breathers. By analyzing the propagation characteristics of the quasi-periodic breathers, these quasi-periodic breathers are divided into three categories, general quasi-periodic breathers, quasi-periodic approximate Kuznetsov–Ma breathers and quasi-periodic Akhmediev breathers. Furthermore, by using an analytical method related to the characteristic lines for the quasi-periodic breathers, the dynamic characteristics including the periods and wave velocities of the quasi-periodic breathers are analyzed.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103449"},"PeriodicalIF":2.1,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747046","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}
This work demonstrated to attain a multiband absorption in the terahertz region with high degree simplification and tunable absorption characteristics. The design model composed of an H-type resonator placed above on a middle layer (dielectric medium) and a metallic layer at the bottom. The single sized resonator strongly interacts with incident electromagnetic wave resulting four near perfect absorption peaks located at 0.625 THz, 1.85 THz, 2.075 THz, and 2.5 THz. Moreover, the suggested design was also investigated for active modulation features by inserting vanadium dioxide (VO2) material into the design metamaterial structure due to which the quad-band absorption profile exhibits a switchable function by variation in the state phase of VO2 from insulator to metallic phase. Therefore, the design structure could have wide range of potential THz technology related field applications.
{"title":"High degree simplification and tunable absorption features of terahertz metamaterial absorber","authors":"Shahzad Anwar , Ghafar Ali , Maaz Khan , Forough Bozorgzadeh","doi":"10.1016/j.wavemoti.2024.103450","DOIUrl":"10.1016/j.wavemoti.2024.103450","url":null,"abstract":"<div><div>This work demonstrated to attain a multiband absorption in the terahertz region with high degree simplification and tunable absorption characteristics. The design model composed of an H-type resonator placed above on a middle layer (dielectric medium) and a metallic layer at the bottom. The single sized resonator strongly interacts with incident electromagnetic wave resulting four near perfect absorption peaks located at 0.625 THz, 1.85 THz, 2.075 THz, and 2.5 THz. Moreover, the suggested design was also investigated for active modulation features by inserting vanadium dioxide (VO2) material into the design metamaterial structure due to which the quad-band absorption profile exhibits a switchable function by variation in the state phase of VO2 from insulator to metallic phase. Therefore, the design structure could have wide range of potential THz technology related field applications.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103450"},"PeriodicalIF":2.1,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747188","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}
Pub Date : 2024-11-16DOI: 10.1016/j.wavemoti.2024.103444
Ben Wilks , Fabien Montiel , Luke G. Bennetts , Sarah Wakes
Eigenmodes are studied for a fluid-filled rectangular tank containing one or more vertical barriers, and on which either Dirichlet or Neumann boundary conditions are prescribed on the lateral walls. In the case where the tank contains a single barrier, the geometry of the tank is equivalent to the unit cell of the cognate periodic array, and its eigenmodes are equivalent to standing Bloch waves. As the submergence depth of the barrier increases, it is shown that the passbands (i.e. frequency intervals in which the periodic array supports Bloch waves) become thinner, and that this effect becomes stronger at higher frequencies. The eigenmodes of a uniform array of vertical barriers in a rectangular tank are also considered. They are found to be a superposition of left- and right-propagating Bloch waves, which couple together at the lateral walls of the tank. A homotopy procedure is used to relate the eigenmodes to the quasimodes of the same uniform array in a fluid of infinite horizontal extent, and the quasimodes are shown to govern the response of the array to incident waves. Qualitative features of the mode shapes are typically preserved by the homotopy, which suggests that the resonant responses of the array in an infinite fluid can be understood in terms of modes of the array in a finite tank.
{"title":"Water wave interactions with surface-piercing vertical barriers in a rectangular tank: Connections with Bloch waves and quasimodes","authors":"Ben Wilks , Fabien Montiel , Luke G. Bennetts , Sarah Wakes","doi":"10.1016/j.wavemoti.2024.103444","DOIUrl":"10.1016/j.wavemoti.2024.103444","url":null,"abstract":"<div><div>Eigenmodes are studied for a fluid-filled rectangular tank containing one or more vertical barriers, and on which either Dirichlet or Neumann boundary conditions are prescribed on the lateral walls. In the case where the tank contains a single barrier, the geometry of the tank is equivalent to the unit cell of the cognate periodic array, and its eigenmodes are equivalent to standing Bloch waves. As the submergence depth of the barrier increases, it is shown that the passbands (i.e. frequency intervals in which the periodic array supports Bloch waves) become thinner, and that this effect becomes stronger at higher frequencies. The eigenmodes of a uniform array of vertical barriers in a rectangular tank are also considered. They are found to be a superposition of left- and right-propagating Bloch waves, which couple together at the lateral walls of the tank. A homotopy procedure is used to relate the eigenmodes to the quasimodes of the same uniform array in a fluid of infinite horizontal extent, and the quasimodes are shown to govern the response of the array to incident waves. Qualitative features of the mode shapes are typically preserved by the homotopy, which suggests that the resonant responses of the array in an infinite fluid can be understood in terms of modes of the array in a finite tank.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103444"},"PeriodicalIF":2.1,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.wavemoti.2024.103452
Ali R. Hadjesfandiari , Gary F. Dargush
Consistent couple stress theory (C-CST) provides the framework for the present investigation of size-dependent effects in the torsional oscillation of elastic circular wires. By using this form of couple stress theory, we are able to develop the first self-consistent size-dependent mechanics solution for this fundamental continuum dynamics problem that satisfies all boundary conditions without approximation. In addition, we derive the dispersion relations and characteristics for torsional waves in C-CST and the natural torsional modes for a finite length wire with fixed ends. Appendices provide a study of the general character of the C-CST eigensolutions and examine the torsional oscillation problem under classical and Mindlin-Tiersten-Koiter couple stress elastodynamics.
{"title":"Size-dependent torsional oscillation of an elastic wire with circular cross-section","authors":"Ali R. Hadjesfandiari , Gary F. Dargush","doi":"10.1016/j.wavemoti.2024.103452","DOIUrl":"10.1016/j.wavemoti.2024.103452","url":null,"abstract":"<div><div>Consistent couple stress theory (C-CST) provides the framework for the present investigation of size-dependent effects in the torsional oscillation of elastic circular wires. By using this form of couple stress theory, we are able to develop the first self-consistent size-dependent mechanics solution for this fundamental continuum dynamics problem that satisfies all boundary conditions without approximation. In addition, we derive the dispersion relations and characteristics for torsional waves in C-CST and the natural torsional modes for a finite length wire with fixed ends. Appendices provide a study of the general character of the C-CST eigensolutions and examine the torsional oscillation problem under classical and Mindlin-Tiersten-Koiter couple stress elastodynamics.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103452"},"PeriodicalIF":2.1,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747044","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}
Pub Date : 2024-11-09DOI: 10.1016/j.wavemoti.2024.103443
Kuldeep Singh , Ioannis Kourakis
The Korteweg–de Vries (KdV) equation can be derived from a plasma-fluid model via a reductive perturbation technique. The associated methodology is summarized, from first principles, focusing on the underlying physical assumptions involved in the plasma-theoretical framework. A beam permeated electron-ion plasma is assumed, although the main findings of this study may be extended to more complicated plasma configurations. Rather counter-intuitively, it is shown that either of the (two) real coefficients appearing in the KdV equation (actually, both depending parametrically on the plasma configuration and on the beam characteristics) may take either positive or negative values, a possibility overlooked in the past. Different possibilities are investigated, from first principles, regarding the sign of the nonlinearity coefficient (that is determined by the electron background statistics, in combination with the beam velocity) and the sign of the dispersion coefficient (that is solely determined by the beam velocity and is always positive in its absence). The possibility of polarity reversal is investigated from first principles, in relation with both the electrostatic potential (pulse) profile and its associated electric field (bipolar pulse) in the electrostatic approximation. Different types of excitations are shown to exist and the role of the (sign of the) various coefficients in the pulse-shaped solution’s propagation characteristics is discussed.
Korteweg-de Vries（KdV）方程可以通过还原扰动技术从等离子体流体模型中推导出来。本文从第一原理出发，总结了相关方法，重点介绍了等离子体理论框架所涉及的基本物理假设。虽然本研究的主要发现可以扩展到更复杂的等离子体配置，但我们还是假设了一种束渗透电子-离子等离子体。与直觉相反的是，研究表明 KdV 方程中出现的（两个）实系数（实际上，这两个系数都取决于等离子体构型和束流特性的参数）既可以取正值，也可以取负值，而这种可能性过去一直被忽视。我们从第一原理出发，研究了非线性系数 A 的符号（由电子背景统计和光束速度共同决定）和色散系数 B 的符号（仅由光束速度决定，在没有光束速度的情况下始终为正）的不同可能性。根据静电近似的静电势（脉冲）剖面及其相关电场（双极脉冲）E=-∇j，从第一原理研究了极性反转的可能性。结果表明存在不同类型的激励，并讨论了各种系数（符号）在脉冲形溶液传播特性中的作用。
{"title":"Generalized analytical solutions of a Korteweg–de Vries (KdV) equation with arbitrary real coefficients: Association with the plasma-fluid framework and physical interpretation","authors":"Kuldeep Singh , Ioannis Kourakis","doi":"10.1016/j.wavemoti.2024.103443","DOIUrl":"10.1016/j.wavemoti.2024.103443","url":null,"abstract":"<div><div>The Korteweg–de Vries (KdV) equation can be derived from a plasma-fluid model via a reductive perturbation technique. The associated methodology is summarized, from first principles, focusing on the underlying physical assumptions involved in the plasma-theoretical framework. A beam permeated electron-ion plasma is assumed, although the main findings of this study may be extended to more complicated plasma configurations. Rather counter-intuitively, it is shown that either of the (two) real coefficients appearing in the KdV equation (actually, both depending parametrically on the plasma configuration and on the beam characteristics) may take either positive or negative values, a possibility overlooked in the past. Different possibilities are investigated, from first principles, regarding the sign of the nonlinearity coefficient <span><math><mi>A</mi></math></span> (that is determined by the electron background statistics, in combination with the beam velocity) and the sign of the dispersion coefficient <span><math><mi>B</mi></math></span> (that is solely determined by the beam velocity and is always positive in its absence). The possibility of polarity reversal is investigated from first principles, in relation with both the electrostatic potential (pulse) profile and its associated electric field (bipolar pulse) <span><math><mrow><mi>E</mi><mo>=</mo><mo>−</mo><mo>∇</mo><mi>ϕ</mi></mrow></math></span> in the electrostatic approximation. Different types of excitations are shown to exist and the role of the (sign of the) various coefficients in the pulse-shaped solution’s propagation characteristics is discussed.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103443"},"PeriodicalIF":2.1,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter , the primary boundary value problem (bvp) is converted to a new bvp for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.
{"title":"Oblique wave propagation over uneven flexible base in a fluid having free-surface tension","authors":"Balaram Sahu , Smrutiranjan Mohapatra , Manas Ranjan Sarangi","doi":"10.1016/j.wavemoti.2024.103433","DOIUrl":"10.1016/j.wavemoti.2024.103433","url":null,"abstract":"<div><div>A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter <span><math><mi>ϵ</mi></math></span>, the primary boundary value problem (<span>bvp</span>) is converted to a new <span>bvp</span> for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103433"},"PeriodicalIF":2.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650916","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}
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