Re[2]: Eliminating unknown functions from partial differential equations
- To: mathgroup at smc.vnet.net
- Subject: [mg41084] Re[2]: [mg41039] Eliminating unknown functions from partial differential equations
- From: Stepan Yakovenko <yakovenko at ngs.ru>
- Date: Thu, 1 May 2003 05:00:30 -0400 (EDT)
- References: <200304300820.EAA25414@smc.vnet.net> <3EAFEDC2.FBF311B2@eunet.at>
- Reply-to: Stepan Yakovenko <yakovenko at ngs.ru>
- Sender: owner-wri-mathgroup at wolfram.com
Hello CAP,
Wednesday, April 30, 2003, 10:37:38 PM, you wrote:
CF> Stepan Yakovenko wrote:
CF> Sorry, but your system seems to be a system of ordinary differential
CF> equation. Your
CF> equations contains ONLY ONE independent variable t. For partial diff.
CF> equ., and how to solve systems of ordinary diff. eq. see:
1) Thanx for the link.
2) I've chosen the simpliest example. One can eliminate \vec H from
Maxwell equations (for optical waveguides):
\nabla \times \vec H = \partial_t \epsilon \vec E
\nabla \times \vec E = -\partial_t \vec H
\nabla \vec \epsilon \vec E = 0
=>
\Delta \vec E + \nabla (\vec E \nabla (\ln \epsilon))=
=-\epsilon \partial_{tt} \vec E
Is it possible to get this result in Mathematica ?
--
Best regards,
Stepan mailto:yakovenko at ngs.ru