Three Classes of Courant-Hilbert Progressive Solutions To the Scalar Wave Equation

References

• Courant , R. and Hilbert , D. 1962 . Methods of Mathematical Physics , Vol. II , New York : Interscience .
   Google Scholar
• Friedlander , F. G. 1946 . Simple progressive solutions of the wave equation . Cambridge Philos. Soc. , 43 : 360 – 373 .
   Google Scholar
• Bombelli , L. , Couch , W. E. and Torrence , R. J. 1991 . Wake-free waves in one and three dimensions . J. Math. Phys. , 32 : 106 – 108 .
   Google Scholar
• Hillion , P. 1999 . Focus wave modes in square-law media . J. Opt. A: Pure Appl. , 1 : 581 – 584 .
   Google Scholar
• Hillion , P. 1999 . High-frequency focus wave modes in uniaxially anisotropic dielectrics . J. Phys. A: Math. Gen. , 32 : 2697 – 2703 .
   Google Scholar
• Hillion , P. 2000 . Propagation of focus wave modes in chiral media . Int. J. Appl. Electrom. Mech. , 10 : 451
   Google Scholar
• Kiselev , A. P. 1999 . Nondispersive edge modes . Wave Motion , 29 : 111 – 117 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• 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 ” . In Progress in Electromagnetic Research, PIER Vol. 19 , 1 – 48 .
   Google Scholar
• Donnelly , D. and Ziolkowski , R. W. 1992 . A method for constructing solutions to homogeneous partial differential equations . Proc. Roy. Soc. London A , 437 : 677 – 692 .
   Google Scholar
• Donnely , D. and Ziolkowski , R. W. 1993 . Designing localized waves . Proc. Roy. Soc. London A , 440 : 541 – 565 .
   Google Scholar
• Bateman , H. 1909 . Proc. London Math. Soc. , 7 : 70
   Google Scholar
• Bateman , H. 1955 . The Mathematical Analysis of Electrical and Optical Wave-Motion on the Basis of Maxwells Equations , New York , NY : Dover .
   Google Scholar
• Hillion , P. 1992 . Courant-Hilbert solutions of the wave equation . J. Math. Phys. , 33 : 2749 – 2753 .
   Web of Science ®Google Scholar
• Hillion , P. 1996 . Distortion-free progressive waves . Europhys. Lett. , 33 : 7 – 10 .
   Google Scholar
• Brittingham , J. N. 1983 . Focus wave modes in homogeneous Maxwell equations: transverse electric mode . J. Appl. Phys. , 54 : 1179 – 1189 .
   Web of Science ®Google Scholar
• Ziolkowski , R. W. 1989 . Localized transmission of electromagnetic energy . Phys. Rev. A , 39 : 2005 – 2033 .
   PubMed Web of Science ®Google Scholar
• Kiselev , A. P. and Perel , M. V. 1997 . “ Qauasiphotons and nondispersive waves ” . In Proc. Day on Diffraction 97 , 86 – 90 . St. Petersburg University Press .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Lu , J. Y. and Greenleaf , J. F. 1992 . Nondiffracting X waves: Exact solutions to free space scalar wave equations and their aperture realizations . IEEE Trans. Ultrason. Ferroelec. Freq. Contr. , 39 : 19 – 31 .
   PubMed Web of Science ®Google Scholar
• Ziolkowski , R. W. , Besieris , I. M. and Shaarawi , A. M. Aperture realizations of exact solutions to homogeneous wave equations . J. Opt. Soc. Am. A , 10 76 – 87 . 1993
   Google Scholar
• Borisov. , V. V. and Kiselev , A. P. 2000 . A new class of relatively undistorted progressive waves . Appl. Math. Lett. , 13 : 83 – 86 .
   Web of Science ®Google Scholar
• MacKinnon , L. 1978 . A nondispersive de Broglie wave packet . Found. Phys. , 8 : 157 – 180 .
   Google Scholar
• Sockel , M. E. 1987 . “ Similarity solutions to nonlinear stochastic equations ” . Virginia Polytechnic Inst. and State Univ . Ph.D. Thesis
   Google Scholar
• Bluman , G. W. and Kumei , S. 1989 . Symmetries and Differential Equations , New York : Springer-Verlag .
   Google Scholar
• Shaarawi , A. M. 1989 . “ Nondispersive wavepackets ” . Virginia Polytechnic Inst. and State Univ . Ph.D. Thesis
   Google Scholar
• Overfelt , P. 1991 . Bessel-Gauss pulses . Phys. Rev. A , 44 : 3941 – 3947 .
   PubMed Web of Science ®Google Scholar
• Sedky , S. M. 1995 . “ Generation of localized waves using dynamic apertures ” . Cairo Univ . M.Sc. thesis
   Google Scholar
• Erdelyi , A. , ed. 1954 . Tables of Integral Transforms , Vol. I , 182 New York : McGraw- Hill .
   Google Scholar
• Heyman , E. 1994 . Pulsed beam propagation in an inhomogeneous medium . IEEE Trans. Antennas Prop. , 42 : 311 – 319 .
   Web of Science ®Google Scholar
• Porras , M. A. , Borghi , R. and Santarsiero , M. 2000 . Few-optical-cycle Bessel-Gauss beams in free space . Phys. Rev. E , 62 : 5729 – 5737 .
   PubMed Web of Science ®Google Scholar
• Besieris , I. M. , Shaarawi , A. M. and Ligthart , L. P. 2000 . A note on dimension reduction and finite energy localized wave solutions to the Klein-Gordon and scalar equations. part I. FWM-Type . J. Electromag. Waves Appl. , 14 : 595 – 612 .
   Google Scholar
• Besieris , I. M. , Shaarawi , A. M. and Ligthart , L. P. 2000 . “ A note on dimension reduction and finite energy localized wave solutions to the Klein-Gordon and scalar equations. part II. X wave-type ” . In Progress in Electromag. Research, PIER Vol. 27 , 357 – 365 .
   Google Scholar