Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Method of residues integration problem

  1. Sep 26, 2009 #1
    Hi all,

    I am trying to determine two Melnikov Integrals (after some manipulation) of the form:
    [tex]\int^{\infty}_{-\infty}cos(at)sech(bt) dt[/tex]
    [tex]\int^{\infty}_{-\infty}cos(at)sech^{3}(bt) dt[/tex]

    The textbook I've been reading (Litchenberg & Libermann), says that the way to integrate similar problems is to use the method of residues. I have a superficial understanding of how that works, but every other time I've used the method of residue I've dealt with rationale functions so that I could find poles and then just apply apply the Cauchy integral formula at the isolated poles.

    Can anyone give me a kick-start on how to begin solving these 2 integrals by the method of residues ?
  2. jcsd
  3. Sep 27, 2009 #2
    Hi thrillhouse86,

    I'm not an expert on the "residue Issue" but here's my suggestion:

    1. Note that both integrands are even functions (at least I think so)
    2. Then complexify the cos-functions, i.e. use the e-function

    3. For the Residue Thm. you will need a special contour. I had posted a similar thread a month ago, I'd try with the same contour:


    PS: post the answer when you have it, I'm interested too :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook