1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Spreading of a pulse as it propagates in a dispersive medium

  1. Feb 13, 2013 #1
    Hello everyone!! Im sorry but i couldnt put this into the template.
    Im studying the spreading of a pulse as it propagates in a dispersive medium, from a well known book. My problem arise when i have to solve an expression.

    Firstly i begin considering that a 1-dim pulse can be written as:


    u(x,t) = 1/2*1/√2∏* ∫A(k)*exp(ikx-iw(k)t) dk + cc (complex conjugate)

    where: k: wave number
    w: angular frecuency



    and then i showed that A(k) can be express in terms of the initial values of the problem, taking into account that w(k)=w(-k) (isotropic medium):

    A(k) = 1/√2∏ ∫ exp(-ikx) * (u(x,0) + i/w(k) * du/dt (x,0)) dx

    I considered du/dt(x,0)=0 wich means that the problems involves 2 pulses with the same amplitud and velocity but oposite directions.
    So A(k) takes the form:

    A(k) = 1/√2∏ ∫ exp(-ikx) * u(x,0)

    Now i take a Gaussian modulated oscilattion as the initial shape of the pulse:

    u(x,0) = exp(-x^2/2L^2) cos(ko x)


    Then the book says that we can easily reach to the expression:

    A(k) = 1/√2∏ ∫ exp(-ikx) exp(-x^2/2L^2) cos (ko x) dx



    = L/2 (exp(-(L^2/2) (k-ko)^2) + exp(-(L^2/2) (k+ko)^2)

    How did he reach to this?? How can i solve this last integral???


    Then, with the expression of A(k) into u(x,t) arise other problem. How can i solve this other integral.


    Thank you very much for helping me!!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Spreading of a pulse as it propagates in a dispersive medium
Loading...