Abstract
This paper presents a brief summary of some of the mathematical techniques that are used in wave front analysis as applied to linear hyperbolic partial differential equations. After an introductory review of the method of classification of partial differential equations, and the identification of wave propagation phenomena, the effects of dispersion on a wave profile are outlined. Thereafter the idea of a characteristic hypersurface is introduced and a little of its differential geometry is examined. Finally, all ideas are drawn together to derive the transport equation which governs the propagation of discontinuities along rays. The appearance of singularities in the solution as a result of focusing effects emerges naturally from a study of the transport equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical Education in Science and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
