The application of the Darboux transformation method to the integrable model of a cylindrically symmetrical chiral field has been considered. The associated linear system of matrix equations has been proposed and the properties of symmetry for its solution obtained. The necessary form of Darboux transformation has been found and formal one- and N-soliton solutions constructed. With the use of Polhmayer's transformation, a sine-Gordon type equation has been given and an hypothesis about its integrability proposed.
{"title":"Darboux transformation and exact solutions for the model of cylindrically symmetrical chiral field","authors":"E. Gutshabash","doi":"10.1109/DD.1999.816183","DOIUrl":"https://doi.org/10.1109/DD.1999.816183","url":null,"abstract":"The application of the Darboux transformation method to the integrable model of a cylindrically symmetrical chiral field has been considered. The associated linear system of matrix equations has been proposed and the properties of symmetry for its solution obtained. The necessary form of Darboux transformation has been found and formal one- and N-soliton solutions constructed. With the use of Polhmayer's transformation, a sine-Gordon type equation has been given and an hypothesis about its integrability proposed.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116531330","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}
Two alternative representations of the wave field in a curved oversized electromagnetic waveguide are discussed: adiabatic modes, matched to the local value of the axis curvature, and full-wave solution of the vectorial parabolic equation. The latter, although being asymptotically equivalent to the adiabatic mode theory, displays additional diffraction effects. A simplified complex WKB analysis is performed in order to estimate residual mode conversion in smooth waveguide bends. Application of the vectorial PE to radio propagation in tunnels is illustrated with numerical examples.
{"title":"Curved oversized EM waveguides: adiabatic modes and parabolic equation","authors":"A. Popov, N. Zhu","doi":"10.1109/DD.1999.816203","DOIUrl":"https://doi.org/10.1109/DD.1999.816203","url":null,"abstract":"Two alternative representations of the wave field in a curved oversized electromagnetic waveguide are discussed: adiabatic modes, matched to the local value of the axis curvature, and full-wave solution of the vectorial parabolic equation. The latter, although being asymptotically equivalent to the adiabatic mode theory, displays additional diffraction effects. A simplified complex WKB analysis is performed in order to estimate residual mode conversion in smooth waveguide bends. Application of the vectorial PE to radio propagation in tunnels is illustrated with numerical examples.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124890951","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 poroacoustic Biot medium is used very often as the admissible approximation for a real oil-filled collector. For such a medium the shear stress of the matrix is equal to zero. In infinite poroacoustic space only fast P-waves and slow P-waves propagate with velocities /spl nu//sub 1/ and /spl nu//sub 2/. The fast wave resulting from the solid and fluid parts moving in phase is similar to the ordinary compressional wave. The slow wave which is the consequence of the solid and fluid part moving out of phase attenuates very rapidly and therefore can not be observed at long distances. Earlier we have shown that an interference slow wave exists in the poroacoustic layer located inside the elastic medium. This wave has very low frequency and velocity and high amplitude. Here we show that in this model a new guided wave exists which has a number of unusual peculiarities.
{"title":"New guided wave in a poroacoustic layer","authors":"P. Krauklis, A. Krauklis","doi":"10.1109/DD.1999.816190","DOIUrl":"https://doi.org/10.1109/DD.1999.816190","url":null,"abstract":"A poroacoustic Biot medium is used very often as the admissible approximation for a real oil-filled collector. For such a medium the shear stress of the matrix is equal to zero. In infinite poroacoustic space only fast P-waves and slow P-waves propagate with velocities /spl nu//sub 1/ and /spl nu//sub 2/. The fast wave resulting from the solid and fluid parts moving in phase is similar to the ordinary compressional wave. The slow wave which is the consequence of the solid and fluid part moving out of phase attenuates very rapidly and therefore can not be observed at long distances. Earlier we have shown that an interference slow wave exists in the poroacoustic layer located inside the elastic medium. This wave has very low frequency and velocity and high amplitude. Here we show that in this model a new guided wave exists which has a number of unusual peculiarities.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131143177","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}
Formation and destruction of waves produced by a source distributed on a specific circle are considered. The circle belongs to the spherical surface, expanding with the velocity of wave perturbation. The wavefunction expansion is constructed in terms of modes in the cylindrical coordinate system. Final results are compared with expressions obtained earlier for the moving circle of a constant radius.
{"title":"Formation and destruction of waves with singularities on the spherical wavefront","authors":"I. Simonenko","doi":"10.1109/DD.1999.816199","DOIUrl":"https://doi.org/10.1109/DD.1999.816199","url":null,"abstract":"Formation and destruction of waves produced by a source distributed on a specific circle are considered. The circle belongs to the spherical surface, expanding with the velocity of wave perturbation. The wavefunction expansion is constructed in terms of modes in the cylindrical coordinate system. Final results are compared with expressions obtained earlier for the moving circle of a constant radius.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128232582","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 Green's function of an electromagnetic field in cholesteric liquid crystals with the pitch being large compared to the wavelength is considered. The Green's function is constructed using the solutions of uniform Maxwell equations. The case of the far zone is analysed in detail. The periodic system is distinguished from an anisotropic medium by a discontinuity of the wave vector surface and a break of beam vector surface. The forbidden zone corresponds to capture of beams with small angles of incidence forming a wave channel. Within this wave channel the Green's function asymptotics differs from 1/r behaviour.
{"title":"Green's function of electromagnetic field in cholesteric liquid crystals with large-scale periodicity","authors":"E. Aksenova, V. Romanov, A. Val'kov","doi":"10.1109/DD.1999.816177","DOIUrl":"https://doi.org/10.1109/DD.1999.816177","url":null,"abstract":"The Green's function of an electromagnetic field in cholesteric liquid crystals with the pitch being large compared to the wavelength is considered. The Green's function is constructed using the solutions of uniform Maxwell equations. The case of the far zone is analysed in detail. The periodic system is distinguished from an anisotropic medium by a discontinuity of the wave vector surface and a break of beam vector surface. The forbidden zone corresponds to capture of beams with small angles of incidence forming a wave channel. Within this wave channel the Green's function asymptotics differs from 1/r behaviour.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132337540","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 two-dimensional Neumann-Kelvin problem describing the steady-state forward motion of a totally submerged tandem is considered in the case when the fluid consists of two superposed layers of different densities and bodies intersect the interface between them. For the so-called least singular solution, examples of non-uniqueness (trapped modes) are constructed using the inverse procedure. This procedure was previously applied by McIver (1996) to the problem of time-harmonic water waves and by Motygin (1997) and Kuznetsov & Motygin (1999) to the least singular and resistanceless statements of the Neumann-Kelvin problem involving a surface-piercing tandem in a homogeneous fluid. In the situation under consideration the inverse method involves investigation of stream lines generated by two vortices placed in the interface. The spacing of vortices delivering trapped modes depends on the forward velocity.
{"title":"On non-uniqueness in the 2D linear problem of a two-layer flow about interface-piercing bodies","authors":"O. Motygin, A. Klimenko","doi":"10.1109/DD.1999.816194","DOIUrl":"https://doi.org/10.1109/DD.1999.816194","url":null,"abstract":"The two-dimensional Neumann-Kelvin problem describing the steady-state forward motion of a totally submerged tandem is considered in the case when the fluid consists of two superposed layers of different densities and bodies intersect the interface between them. For the so-called least singular solution, examples of non-uniqueness (trapped modes) are constructed using the inverse procedure. This procedure was previously applied by McIver (1996) to the problem of time-harmonic water waves and by Motygin (1997) and Kuznetsov & Motygin (1999) to the least singular and resistanceless statements of the Neumann-Kelvin problem involving a surface-piercing tandem in a homogeneous fluid. In the situation under consideration the inverse method involves investigation of stream lines generated by two vortices placed in the interface. The spacing of vortices delivering trapped modes depends on the forward velocity.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121923748","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}
Full-wave electromagnetic interaction of two regular arrays of dipole scatterers is considered. To calculate the local field acting on a particle in arrays a method analogous to the Lorenz-Lorentz approach is used. The full-wave formulas representing the fields created by a continuous distribution sheet with a circular hole of a certain radius are obtained for the case when the observation point is located on the hole axis at an arbitrary distance from the hole center. A simple analytical approach to calculate the interaction field in dense arrays is developed. From the energy conservation principle, the exact expression for the imaginary part of interaction constants in regular arrays is established. As an application example illustrating the physical aspects of the obtained results, the reflection from a double array of electrically polarizable particles is considered. An explicit analytical solution for the reflection coefficient is given.
{"title":"Electromagnetic diffraction by double arrays of dipole scatterers","authors":"V. Yatsenko, S. Maslovski","doi":"10.1109/DD.1999.816201","DOIUrl":"https://doi.org/10.1109/DD.1999.816201","url":null,"abstract":"Full-wave electromagnetic interaction of two regular arrays of dipole scatterers is considered. To calculate the local field acting on a particle in arrays a method analogous to the Lorenz-Lorentz approach is used. The full-wave formulas representing the fields created by a continuous distribution sheet with a circular hole of a certain radius are obtained for the case when the observation point is located on the hole axis at an arbitrary distance from the hole center. A simple analytical approach to calculate the interaction field in dense arrays is developed. From the energy conservation principle, the exact expression for the imaginary part of interaction constants in regular arrays is established. As an application example illustrating the physical aspects of the obtained results, the reflection from a double array of electrically polarizable particles is considered. An explicit analytical solution for the reflection coefficient is given.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"27 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":"134301389","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 problem of plane wave scattering on a strip or on a set of strips located in a plane is under consideration. A functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived. It is shown that the solution of the problem (the spectrum of the scattered field) is a solution of an ordinary differential equation (ODE). The coefficients of the ODE are known up to several constants. The restrictions enabling one to determine the constants are discussed. Thus, the problem of diffraction by strips is reduced to the problem of finding the constants and solving the ODE, but not the integral equation.
{"title":"An extension of Wiener-Hopf method: ordinary differential equations associated with diffraction problems","authors":"A. Shanin","doi":"10.1109/DD.1999.816198","DOIUrl":"https://doi.org/10.1109/DD.1999.816198","url":null,"abstract":"The problem of plane wave scattering on a strip or on a set of strips located in a plane is under consideration. A functional equation of Wiener-Hopf type with analytical restrictions on unknown functions is derived. It is shown that the solution of the problem (the spectrum of the scattered field) is a solution of an ordinary differential equation (ODE). The coefficients of the ODE are known up to several constants. The restrictions enabling one to determine the constants are discussed. Thus, the problem of diffraction by strips is reduced to the problem of finding the constants and solving the ODE, but not the integral equation.","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":"129389849","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 higher-times approach to construction of finite-gap solutions of the Harry Dim equation has been improved. It is based on an explicit representation of conservation laws' fluxes as differential polynomials. In the stationary limit along with well-known smooth densities also some new singular one- and two-gap densities of the polar operator associated with the Harry Dim equation have been built. The procedure of reduction of one- and two-gap densities into the soliton sector has been verified.
{"title":"Spectral properties of polar operators with finite-gap elliptic densities","authors":"L. Dmitrieva, D.A. Pyatkin","doi":"10.1109/DD.1999.816180","DOIUrl":"https://doi.org/10.1109/DD.1999.816180","url":null,"abstract":"The higher-times approach to construction of finite-gap solutions of the Harry Dim equation has been improved. It is based on an explicit representation of conservation laws' fluxes as differential polynomials. In the stationary limit along with well-known smooth densities also some new singular one- and two-gap densities of the polar operator associated with the Harry Dim equation have been built. The procedure of reduction of one- and two-gap densities into the soliton sector has been verified.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"21 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":"117241906","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 study the elliptic-hyperbolic Davey-Stewartson equation which is considered as a nonlocal nonlinear Schrodinger equation with nonlinearities involving derivatives of unknown function in two space dimensions. We show that solutions become analytic for any t/spl ne/0 with respect to x if the data are small and decay exponentially when |x|/spl rarr//spl infin/.
{"title":"Analytic smoothing effect and global existence for elliptic hyperbolic Davey-Stewartson system","authors":"N. Hayashi, H. Uchida, P. Naumkin","doi":"10.1109/DD.1999.816184","DOIUrl":"https://doi.org/10.1109/DD.1999.816184","url":null,"abstract":"We study the elliptic-hyperbolic Davey-Stewartson equation which is considered as a nonlocal nonlinear Schrodinger equation with nonlinearities involving derivatives of unknown function in two space dimensions. We show that solutions become analytic for any t/spl ne/0 with respect to x if the data are small and decay exponentially when |x|/spl rarr//spl infin/.","PeriodicalId":275823,"journal":{"name":"International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367)","volume":"123 1 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":"131361356","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}
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