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Nonlinear Dispersion Relation with Imaginary Part

  1. Sep 25, 2014 #1
    1. The problem statement, all variables and given/known data
    I've determined the dispersion relation for a particular traveling wave and have found that it contains both a real and an imaginary part. So, I let [itex]k=\alpha+i\beta[/itex] and solved for [itex]\alpha[/itex] and [itex]\beta[/itex]

    I found that there are [itex]\pm[/itex] signs in the solutions for both [itex]\alpha[/itex] and [itex]\beta[/itex].

    Considering the two different cases for both [itex]\alpha[/itex] and [itex]\beta[/itex], I find:

    For a: if +, then [itex]\alpha=\frac{\omega}{c}[/itex]. If -, [itex]\alpha=0[/itex]

    For b: if +, then [itex]\beta=\frac{\omega}{c*\sqrt2}[/itex]. If -, [itex]\beta=\frac{\omega}{c*\sqrt2}+\sqrt2[/itex]

    How am I supposed to decide which of the roots (either positive or negative) to use for each?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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