Abstract
We prove that the homogeneous wave equation has different kinds of nondispersive solutions all defined in terms of an arbitrary functionF(u), whereu is a solution of the corresponding characteristic equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bateman, H.:Partial Differential Equations of Mathematical Physics, Cambridge Univ. Press (1959).
Brittingham, J. N.: Focus wave modes in homogeneous Maxwell's equations,J. Appl. Phys. 54 (1983), 1179.
Courant, R. and Hubert, D.:Methods of Mathematical Physics, Vol. 2, Interscience, New York (1962).
Deschamps, G.: Gaussian beams as a bundle of complex rays,Electr. Lett. 7 (1971), 684.
Enziger, P. D. and Raz, S.: Wave solutions under complex space-time shift,J. Opt. Soc. Amer. A 4, 3 (1987).
Heyman, E. and Felsen, L. B.: Complex source pulsed beam fields,J. Opt. Soc. Amer. A 6, 8 (1989).
Hillion, P.: The Goursat problem for the wave equation,J. Math. Phys. 31, 1939 (1990).
Kiselev, A. P.: Modulated gaussian beams,Radiofisika 26, 1014 (1983).
Landau, L. D. and Lifschitz, E. M.:Fluid Mechanics, Pergamon, Oxford (1959).
Marchai, C.: Solutions générales des équations de Maxwell dans le vide,Onde Electrique 71(6), 61 (1991).
Morse, P. M. and Feschbach, H.:Methods of Theoretical Physics, McGraw Hill, New York (1953).
Sezginer, A. A.: General formulation of the focus wave modes,J. Appl. Phys. 57, 678 (1985).
Stieltjes, T. J.: Sur les solutions de l'équation d'onde,C.R. Acad. Sci. 95, 901 (1882).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hillion, P. Generalized phases and nondispersive waves. Acta Appl Math 30, 35–45 (1993). https://doi.org/10.1007/BF00993341
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00993341