root-finding

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#497

From: ramesh
Date: Fri, 11 Sep 1992 04:43

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I have been trying to find the roots of the following complex valued dispersion
relation for its complex roots w:

1 - b*((j*(m-w)+x)*(1-exp(-x+j*(m-w))) + (-j*(m+w)+x)*(1-exp(-(x+j*(m+w)))) =0
        _____________________________      _______________________________
                  (m-w)**2+x**2                     (m+w)**2+x**2


I have been able to find roots for x large and positive (dropping the exponent)
but i don't have any result for a general solution

Another way to write this is to let w = u + j*d where u and d  are real.  Then
substituting we obtain two equations for the unknowns u and d.  Howver this
does not really help, all it does is replace the exponential with sinusoids in
u.   

Does anyone have any ideas on what to do?  I haven't even been able to
visualize the function.    Any suggestions will be greatly appreciated.   

Thanks


Ramesh

Ramesh@mv3600.bmen.tulane.edu

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From: ramesh@MV3600.BMEN.TULANE.EDU
Subject: root-finding
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Date: Fri, 11 Sep 1992 04:43:32 GMT
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