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Articles

A Note On Dimension Reduction and Finite Energy Localized Wave Solutions To the Klein-Gordon and Scalar Wave Equations. Part I. Fwm-Type

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Pages 593-610 | Published online: 03 Apr 2012

References

  • Bateman , H. 1909 . Proc. London Math. Soc. , 7 : 70
  • Bateman , H. 1955 . The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwell's Equations Dover, New York , NY
  • Donnely , R. and Ziolkowski , R. W. 1992 . A method for constructing solutions to homogeneous partial differential equations . Proc. Roy. Soc. , : 677 – 692 . London A 437
  • Donnely , R. and Ziolkowski , R. W. 1993 . Designing localized waves . Proc. Roy. Soc. , : 541 – 565 . London A 440
  • Besieris , I. M. , Shaarawi , A. M. and Ziolkowski , R. W. 1989 . A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation . J. Math. Phys. , 30 : 1254 – 1269 .
  • Besieris , I. M. , Abdel-Rahman , M. , Shaarawi , A. M. and Chatzipetros , A. 1998 . Two fundamental representations of localized pulse solutions to the scalar wave equation . Progress in Electromagnetic Research , : 1 – 48 . PIER 19
  • Magnus , W. , Oberhettinger , F. and Soni , R. P. 1966 . Formulas and Theorems for the Special Functions of Mathematical Physics , Vol. 93 , New York , NY : Springer-Verlag .
  • Ziolkowski , R. W. 1985 . Exact solutions of the wave equation with complex source locations . J. Math. Phys. , 26 : 861 – 863 .
  • Brittingham , J. N. 1983 . Focus wave modes in homogeneous Maxwell equations: transverse electric mode . J. Appl. Phys. , 54 : 1179 – 1189 .
  • Rahman , A. M. , Besieris , I. M. and Shaarawi , A. M. 1998 . A comprehensive analysis of propagation of localized waves in collisionless plasma media . J. Electromag. Waves Appl. , 11 : 1649 – 1668 .
  • Ziolkowski , R. W. 1989 . Localized transmission of electromagnetic energy . Phys. Rev. , : 2005 – 2033 . A 39
  • Shaarawi , A. M. , Besieris , I. M. and Ziolkowski , R. W. 1990 . A novel approach to the synthesis of nondispersive wavepacket solutions to the Klein-Gordon and Dirac equations . J. Math. Phys. , 31 : 2511 – 2519 .
  • Prudnikov , A. P. , Brychov , Yu. A. and Marichev , O. I. 1952 . “ Integrals and Series ” . In Direct Laplace Transforms , Vol. 4 , New York , NY : Gordon and Breach Science Publishers . 31
  • Shvartsburg , A. B. 1996 . Time-Domain Optics of Ultrashort Waveforms , Oxford : Clarendon Press .
  • Kiselev , A. P. and Perel , M. V. 1997 . “ Quasiphotons and nondispersive waves ” . In Proc. Day on Diffraction '97 , 86 – 90 . St. Petersburg University Press .
  • Feng , S. , Winful , H. G. and Hellwarth , R. W. 1999 . Spatio-temporal evolution of focused single-cycle electromagnetic pulses . Phys. Rev. E , 59 : 4630 – 4649 .
  • Heyman , E. 1994 . Pulsed beam propagation in an inhomogeneous medium . IEEE Trans. Antennas Propag. , 42 : 311 – 319 .
  • Porras , A. M. 1998 . Ultrashort pulsed Gaussian light beams . Phys. Rev. E. , 58 : 1096 – 1093 .
  • Hillion , P. 1994 . Paraxial Maxwell's equations . Opt. Comm. , 107 : 327
  • Melamed , T. and Felsen , L. P. 1998 . Pulsed beam propagation in lossless dispersive media. 1. Theory . J. Opt. Soc. Am. , A 15 : 1268 – 1276 . Pulsed beam propagation in lossless dispersive media. 2. Applications," J. Opt. Soc. Am. A 15, 1277–1284, 1998
  • Shaarawi , A. M. 1989 . Nondispersive Wavepackets , Virginia Polytechnic Inst. and State Univ . Ph.D. thesis
  • Overfelt , P. L. 1991 . Bessel-Gauss pulses . Phys. Rev. , A 44 : 3941 – 3947 .
  • Sedky , S. M. 1995 . Generation of Localized Waves Using Dynamic Apertures , Cairo Univ . M.Sc. thesis

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