- #1
Chen
- 977
- 1
Hi,
I'm reading the following paper:
http://prola.aps.org/abstract/PR/v127/i6/p1918_1
(It's physics, you don't really have to click that)
Somewhere along the way the authors make a transition that I can't understand. Basically they have an ODE (5.9), which is integrated to give equation (5.10). Then they define a new function, y2, to replace the original function, v2, and find a new integral equation for it (5.14). I'm bringing two screen shots from the article that show this transition. The only other thing you need to know is that v2a, v2b and v2c are the roots of the expression insider the root in the integral of (5.10).
Screen shots: (in order)
http://img59.imageshack.us/img59/1887/partajj6.png
http://img62.imageshack.us/img62/5359/partbyc9.png
Now, I tried following this transition myself and couldn't make any sense of it. Most of all, I don't understand how the final integral equation (5.14) has y in the limits of integration, and not y2 or something like that.
Help, please?
Thanks,
Chen
I'm reading the following paper:
http://prola.aps.org/abstract/PR/v127/i6/p1918_1
(It's physics, you don't really have to click that)
Somewhere along the way the authors make a transition that I can't understand. Basically they have an ODE (5.9), which is integrated to give equation (5.10). Then they define a new function, y2, to replace the original function, v2, and find a new integral equation for it (5.14). I'm bringing two screen shots from the article that show this transition. The only other thing you need to know is that v2a, v2b and v2c are the roots of the expression insider the root in the integral of (5.10).
Screen shots: (in order)
http://img59.imageshack.us/img59/1887/partajj6.png
http://img62.imageshack.us/img62/5359/partbyc9.png
Now, I tried following this transition myself and couldn't make any sense of it. Most of all, I don't understand how the final integral equation (5.14) has y in the limits of integration, and not y2 or something like that.
Help, please?
Thanks,
Chen
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