Transient waves produced by a source on a circle of a constant radius which starts its motion at a fixed moment of time and moves along an infinite straight line with a constant velocity greater than the wavefront velocity (the velocity of light for electromagnetic waves) are considered.
{"title":"Formation of waves by a source distributed on a superluminal circle","authors":"V. Borisov","doi":"10.1109/DD.1999.816178","DOIUrl":"https://doi.org/10.1109/DD.1999.816178","url":null,"abstract":"Transient waves produced by a source on a circle of a constant radius which starts its motion at a fixed moment of time and moves along an infinite straight line with a constant velocity greater than the wavefront velocity (the velocity of light for electromagnetic waves) are considered.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114338190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze the dynamics of seismic waves in a ray series approximation in the time domain. The aims of the research are: to describe the wave field in a first approximation of ray series (that is to take into account two first terms) and to consider singular situations of the ray propagation. We suggest a new technique of elastic wave field calculation in the ray series approximation. Some explicit formulas were received for regular cases of wave propagation. It was shown that on the simple and cusp caustics a conventional ray series (orders: q, q+1,...) which is valid far from caustics splits into two ray series (orders: q-/spl alpha/, q+1-/spl alpha/,... and q+/spl alpha/, q+1+/spl alpha/,...). For cusp caustics a uniform wave field description was developed that is valid on the caustic itself and out of it.
{"title":"Method of discontinuities and integral representation in the analysis of wave field dynamics","authors":"S. Goldin, A. Duchkov","doi":"10.1109/DD.1999.816181","DOIUrl":"https://doi.org/10.1109/DD.1999.816181","url":null,"abstract":"We analyze the dynamics of seismic waves in a ray series approximation in the time domain. The aims of the research are: to describe the wave field in a first approximation of ray series (that is to take into account two first terms) and to consider singular situations of the ray propagation. We suggest a new technique of elastic wave field calculation in the ray series approximation. Some explicit formulas were received for regular cases of wave propagation. It was shown that on the simple and cusp caustics a conventional ray series (orders: q, q+1,...) which is valid far from caustics splits into two ray series (orders: q-/spl alpha/, q+1-/spl alpha/,... and q+/spl alpha/, q+1+/spl alpha/,...). For cusp caustics a uniform wave field description was developed that is valid on the caustic itself and out of it.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115876428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current behavior on an infinitely long, perfectly conducting, circular cylinder immersed in a uniform magnetoplasma, in which the superimposed static magnetic field is parallel to the axis of the cylinder, is studied. The currents on the cylinder are excited by the delta-gap source with the given time-harmonic voltage. A rigorous representation is obtained for the current distribution on the cylinder. Generally, the surface current on the cylinder can consist of a bound (proper) mode and improper radiation modes which constitute a continuous-spectrum part of the current. The current distribution along a cylinder whose radius varies gradually with distance from the feed gap is also analyzed.
{"title":"Current behavior on a perfectly conducting cylinder with a delta-gap excitation in an anisotropic medium","authors":"A. Kudrin, E. Petrov, T. Zaboronkova","doi":"10.1109/DD.1999.816202","DOIUrl":"https://doi.org/10.1109/DD.1999.816202","url":null,"abstract":"The current behavior on an infinitely long, perfectly conducting, circular cylinder immersed in a uniform magnetoplasma, in which the superimposed static magnetic field is parallel to the axis of the cylinder, is studied. The currents on the cylinder are excited by the delta-gap source with the given time-harmonic voltage. A rigorous representation is obtained for the current distribution on the cylinder. Generally, the surface current on the cylinder can consist of a bound (proper) mode and improper radiation modes which constitute a continuous-spectrum part of the current. The current distribution along a cylinder whose radius varies gradually with distance from the feed gap is also analyzed.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116460621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A two-dimensional body moves forward with constant velocity in an inviscid incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body intersects an interface between the layers. The boundary-value problem for the velocity potential is considered in the framework of linearized water-wave theory. A pair of physically justified supplementary conditions is introduced at points where the body intersects the interface. The extended problem is shown to be well-posed and reduced to an integro-algebraic system. Total resistance to the body motion is found using the asymptotics of the solution at infinity.
{"title":"The two-dimensional Neumann-Kelvin problem for an interface-intersecting body in a two-layer fluid","authors":"A. Klimenko","doi":"10.1109/DD.1999.816189","DOIUrl":"https://doi.org/10.1109/DD.1999.816189","url":null,"abstract":"A two-dimensional body moves forward with constant velocity in an inviscid incompressible fluid under gravity. The fluid consists of two layers having different densities, and the body intersects an interface between the layers. The boundary-value problem for the velocity potential is considered in the framework of linearized water-wave theory. A pair of physically justified supplementary conditions is introduced at points where the body intersects the interface. The extended problem is shown to be well-posed and reduced to an integro-algebraic system. Total resistance to the body motion is found using the asymptotics of the solution at infinity.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128051141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The boundary value problem is bounded in the space variable domain with mixed boundary conditions for the Rossby wave equation. We concentrated our attention on the asymptotic property of the solution. Thus we examined the single domain for n=2 and proved the necessary basic property of eigenfunctions.
{"title":"The asymptotic behaviour for large values of the time of energy of boundary value problem with mixed boundary conditions for Rossby wave equation","authors":"I. Ogorodnikov","doi":"10.1109/DD.1999.816196","DOIUrl":"https://doi.org/10.1109/DD.1999.816196","url":null,"abstract":"The boundary value problem is bounded in the space variable domain with mixed boundary conditions for the Rossby wave equation. We concentrated our attention on the asymptotic property of the solution. Thus we examined the single domain for n=2 and proved the necessary basic property of eigenfunctions.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129444609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Boiti, F. Pempinelli, B. Prinari, A.K. Pogrebkov
We try to generalize the inverse scattering transform (IST) for the Kadomtsev-Petviashvili (KPI) equation to the case of potentials with "ray" type behavior, that is non-decaying along a finite number of directions in the plane. We present here the special but rather wide subclass of such potentials obtained by applying recursively N binary Backlund transformations to a decaying potential. We start with a regular rapidly decaying potential for which all elements of the direct and inverse problem are given. We introduce an exact recursion procedure for an arbitrary number of binary Backlund transformations and corresponding Darboux transformations for Jost solutions and solutions of the discrete spectrum. We show that Jost solutions obey modified integral equations and present their analytical properties. We formulate conditions of reality and regularity of the potentials constructed by these means and derive spectral data of the transformed Jost solutions. Finally we solve the recursion procedure getting a solution which describes N solitons superimposed to a generic background.
{"title":"N-wave soliton solution on a generic background for KPI equation","authors":"M. Boiti, F. Pempinelli, B. Prinari, A.K. Pogrebkov","doi":"10.1109/DD.1999.816197","DOIUrl":"https://doi.org/10.1109/DD.1999.816197","url":null,"abstract":"We try to generalize the inverse scattering transform (IST) for the Kadomtsev-Petviashvili (KPI) equation to the case of potentials with \"ray\" type behavior, that is non-decaying along a finite number of directions in the plane. We present here the special but rather wide subclass of such potentials obtained by applying recursively N binary Backlund transformations to a decaying potential. We start with a regular rapidly decaying potential for which all elements of the direct and inverse problem are given. We introduce an exact recursion procedure for an arbitrary number of binary Backlund transformations and corresponding Darboux transformations for Jost solutions and solutions of the discrete spectrum. We show that Jost solutions obey modified integral equations and present their analytical properties. We formulate conditions of reality and regularity of the potentials constructed by these means and derive spectral data of the transformed Jost solutions. Finally we solve the recursion procedure getting a solution which describes N solitons superimposed to a generic background.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116858180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：