Pub Date : 2024-11-28DOI: 10.1016/j.wavemoti.2024.103455
Majid Madadi , Mustafa Inc
This work investigates new exact solutions within a unique (2+1)-dimensional problem by combining the Hirota bilinear forms of the Kadomtsev–Petviashvili and the Shallow Water Wave equations. We obtain resonant Y-type and X-type soliton, breather, and lump waves by introducing novel limitations on the -soliton. Additionally, it generates various types of solutions (bulk-soliton, fissionable soliton-lump, breather-lump, and soliton-breather-lump) based on velocity and module resonance conditions. Furthermore, we investigate the lump wave’s paths interacting with the waves prior to and following collision using the long-wave limit approach. We show that the lump wave either avoids collision with other waves or maintains a persistent state of collision with them by applying additional limitations. Specifically, we provide a series of figures depicting all solutions, comprehensively capturing their dynamical behavior and interactions.
{"title":"Dynamics of localized waves and interactions in a (2+1)-dimensional equation from combined bilinear forms of Kadomtsev–Petviashvili and extended shallow water wave equations","authors":"Majid Madadi , Mustafa Inc","doi":"10.1016/j.wavemoti.2024.103455","DOIUrl":"10.1016/j.wavemoti.2024.103455","url":null,"abstract":"<div><div>This work investigates new exact solutions within a unique (2+1)-dimensional problem by combining the Hirota bilinear forms of the Kadomtsev–Petviashvili and the Shallow Water Wave equations. We obtain resonant Y-type and X-type soliton, breather, and lump waves by introducing novel limitations on the <span><math><mi>N</mi></math></span>-soliton. Additionally, it generates various types of solutions (bulk-soliton, fissionable soliton-lump, breather-lump, and soliton-breather-lump) based on velocity and module resonance conditions. Furthermore, we investigate the lump wave’s paths interacting with the waves prior to and following collision using the long-wave limit approach. We show that the lump wave either avoids collision with other waves or maintains a persistent state of collision with them by applying additional limitations. Specifically, we provide a series of figures depicting all solutions, comprehensively capturing their dynamical behavior and interactions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103455"},"PeriodicalIF":2.1,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746292","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 : 2024-11-22DOI: 10.1016/j.wavemoti.2024.103454
Călin-Iulian Martin , Emilian I. Părău
We present a Hamiltonian formulation of two-dimensional hydroelastic waves propagating at the free surface of a stratified rotational ideal fluid of finite depth, covered by a thin ice sheet. The flows considered exhibit a discontinuous stratification and piecewise constant vorticity, accommodating the presence of interfaces and of linearly sheared currents.
{"title":"Hamiltonian formulation for interfacial periodic waves propagating under an elastic sheet above stratified piecewise constant rotational flow","authors":"Călin-Iulian Martin , Emilian I. Părău","doi":"10.1016/j.wavemoti.2024.103454","DOIUrl":"10.1016/j.wavemoti.2024.103454","url":null,"abstract":"<div><div>We present a Hamiltonian formulation of two-dimensional hydroelastic waves propagating at the free surface of a stratified rotational ideal fluid of finite depth, covered by a thin ice sheet. The flows considered exhibit a discontinuous stratification and piecewise constant vorticity, accommodating the presence of interfaces and of linearly sheared currents.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103454"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747052","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 : 2024-11-21DOI: 10.1016/j.wavemoti.2024.103456
C. Senthil Kumar , R. Radha
In this paper, we analyse the (3+1) dimensional Bogoyavlensky–Konopelchenko equation. Using Painlevé Truncation approach, we have constructed solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the solution, we have generated physically interesting solutions like periodic solutions, kinks, linear rogue waves, line lumps, dipole lumps and hybrid dromions. It is interesting to note that unlike in (2+1) dimensional nonlinear partial differential equations, the line lumps interact and undergo elastic collision without exchange of energy which is confirmed by the asymptotic analysis. The hybrid dromions are also found to retain their amplitudes during interaction undergoing elastic collision. The highlight of the results is that one also observes the two nonparallel ghost solitons as well whose intersection gives rise to hybrid dromions, a phenomenon not witnessed in (2+1) dimensions.
{"title":"Exotic coherent structures and their collisional dynamics in a (3+1) dimensional Bogoyavlensky–Konopelchenko equation","authors":"C. Senthil Kumar , R. Radha","doi":"10.1016/j.wavemoti.2024.103456","DOIUrl":"10.1016/j.wavemoti.2024.103456","url":null,"abstract":"<div><div>In this paper, we analyse the (3+1) dimensional Bogoyavlensky–Konopelchenko equation. Using Painlevé Truncation approach, we have constructed solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the solution, we have generated physically interesting solutions like periodic solutions, kinks, linear rogue waves, line lumps, dipole lumps and hybrid dromions. It is interesting to note that unlike in (2+1) dimensional nonlinear partial differential equations, the line lumps interact and undergo elastic collision without exchange of energy which is confirmed by the asymptotic analysis. The hybrid dromions are also found to retain their amplitudes during interaction undergoing elastic collision. The highlight of the results is that one also observes the two nonparallel ghost solitons as well whose intersection gives rise to hybrid dromions, a phenomenon not witnessed in (2+1) dimensions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103456"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747049","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 : 2024-11-21DOI: 10.1016/j.wavemoti.2024.103453
P. Panayotaros , R.M. Vargas-Magaña
We study gravity water waves in a domain with inclined lateral boundaries that make a °angle with the horizontal axis. We consider free surface potential flow and a simplified model that contains quadratic nonlinear interactions among the normal modes. The particular geometry leads to classical semi-explicit expressions for the normal modes and frequencies, and we use this information to compute the mode interaction coefficients. We further use a partial normal form to compute the amplitude dependence of nonlinear frequency correction of the lowest frequency mode. We indicate the general computation and present numerical results for a truncations to a system for the two lowest modes.
{"title":"Low mode interactions in water wave model in triangular domain","authors":"P. Panayotaros , R.M. Vargas-Magaña","doi":"10.1016/j.wavemoti.2024.103453","DOIUrl":"10.1016/j.wavemoti.2024.103453","url":null,"abstract":"<div><div>We study gravity water waves in a domain with inclined lateral boundaries that make a <span><math><mrow><mn>45</mn></mrow></math></span>°angle with the horizontal axis. We consider free surface potential flow and a simplified model that contains quadratic nonlinear interactions among the normal modes. The particular geometry leads to classical semi-explicit expressions for the normal modes and frequencies, and we use this information to compute the mode interaction coefficients. We further use a partial normal form to compute the amplitude dependence of nonlinear frequency correction of the lowest frequency mode. We indicate the general computation and present numerical results for a truncations to a system for the two lowest modes.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103453"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746293","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 : 2024-11-21DOI: 10.1016/j.wavemoti.2024.103451
A.P. Misra, Gadadhar Banerjee
The formation of thermoacoustic shocks is studied in a fluid complex plasma. The thermoacoustic wave mode can be damped (or anti-damped) when the contribution from the thermoacoustic interaction is lower (or higher) than that due to the particle collision and/or the kinematic viscosity. In the nonlinear regime, the thermoacoustic wave, propagating with the acoustic speed, can evolve into small amplitude shocks whose dynamics are governed by the Bateman-Burgers equation with an additional nonlinear term that appears due to the particle collision and nonreciprocal interactions of charged particles providing the thermal feedback. The appearance of such nonlinearity can cause the shock fronts to be stable (or unstable) depending on the collision frequency remains below (or above) a critical value and the thermal feedback is positive. The existence of different kinds of shocks and their characteristics are analyzed analytically and numerically with the system parameters that characterize the thermal feedback, thermal diffusion, heat capacity per fluid particle, the particle collision and the fluid viscosity. A good agreement between analytical and numerical results is also noticed.
{"title":"Analytical and numerical study of plane progressive thermoacoustic shock waves in complex plasmas","authors":"A.P. Misra, Gadadhar Banerjee","doi":"10.1016/j.wavemoti.2024.103451","DOIUrl":"10.1016/j.wavemoti.2024.103451","url":null,"abstract":"<div><div>The formation of thermoacoustic shocks is studied in a fluid complex plasma. The thermoacoustic wave mode can be damped (or anti-damped) when the contribution from the thermoacoustic interaction is lower (or higher) than that due to the particle collision and/or the kinematic viscosity. In the nonlinear regime, the thermoacoustic wave, propagating with the acoustic speed, can evolve into small amplitude shocks whose dynamics are governed by the Bateman-Burgers equation with an additional nonlinear term that appears due to the particle collision and nonreciprocal interactions of charged particles providing the thermal feedback. The appearance of such nonlinearity can cause the shock fronts to be stable (or unstable) depending on the collision frequency remains below (or above) a critical value and the thermal feedback is positive. The existence of different kinds of shocks and their characteristics are analyzed analytically and numerically with the system parameters that characterize the thermal feedback, thermal diffusion, heat capacity per fluid particle, the particle collision and the fluid viscosity. A good agreement between analytical and numerical results is also noticed.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"133 ","pages":"Article 103451"},"PeriodicalIF":2.1,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747050","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.2024.103448
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}
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