most recent 30 from http://mathoverflow.net 2013-05-25T12:29:26Z http://mathoverflow.net/feeds/user/9880 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation nikofeyn 2010-10-07T20:22:59Z 2010-11-19T04:22:13Z

<p>i am trying to find resources on the derivation of the fundamental solution to the radial wave equation. any suggestions of or links to books, papers, and/or notes would be much appreciated. i have tried searching google, arxiv, etc. for information, but i haven't come up with anything useful yet. there's a lot of material pertaining to physics concerning using the solution, but i need the derivation.</p> <p>i've been learning about solutions to the wave equation for euclidean dimensions 1-3 (d'Alembert's formula, spherical means, method of descent), and the above is my next task. if you have any general insight about the radial wave equation, this would be helpful as well. thanks!</p> <p>(background: 3rd year graduate student in mathematics)</p> <p><strong>edit</strong>: if no one has any specific references to the derivation, then what about context? does the spherically symmetric wave equation mean the same thing as the radial wave equation? i know that seems like a possibly ignorant question, but to someone unfamiliar with or new to this, i think it's good to be cautious and not say well they sound the same.</p>

http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation/41456#41456 nikofeyn 2010-10-08T00:47:05Z 2010-10-08T00:47:05Z

i'll take a look at this, although the notation seems like it might take some work. thank you for the link.

http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation nikofeyn 2010-10-08T00:46:12Z 2010-10-08T00:46:12Z

i don't think the methods translate between the two. i have selberg's notes already, but it's not in there. my professor specifically mentioned this. also, i noted that i've already investigated the spherical means approach, so knowing this, i would find it strange that i was told to look at the radial equation if it just required the same method. i was also told it was not easy. sogge's book looks to talk about spherically symmetric systems (what's meant by radial?), so i'll take a look at it.

http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation/41454#41454 nikofeyn 2010-10-08T00:29:28Z 2010-10-08T00:29:28Z

i'm not familiar with the specifics, as evidenced by this post, but i think it was clear that i meant as general of an approach as possible to solving the radial wave equation.

http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation/41454#41454 nikofeyn 2010-10-07T21:09:25Z 2010-10-07T21:09:25Z

thank you for the response. i have griffiths' book, but i am really needing a more mathematical treatment, as right now the physical applications aren't the goal. for instance, my professor mentioned the use of some sort of kernel (heat?, dirichlet?). now these are just things he very briefly mentioned so what he meant i don't know, but i need as general of an approach as possible.

http://mathoverflow.net/questions/41449/fundamental-solution-of-radial-wave-equation nikofeyn 2010-10-07T20:33:40Z 2010-10-07T20:33:40Z

someone giving the derivation here would work. this isn't for a course or anything, but i just need to learn it and work through it myself. i am just really not for sure of the idea/approach needed or motivation, other than i guess the equation governs waves whose amplitude only depends on the radial distance from the origin. i don't know if there are different methods depending on the dimension, but the 3-dimensional case or as general solution as possible would be best. thank you for the response.