# Homework Help: Nonlinear Dispersion Relation with Imaginary Part

1. Sep 25, 2014

### rmjmu507

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 $k=\alpha+i\beta$ and solved for $\alpha$ and $\beta$

I found that there are $\pm$ signs in the solutions for both $\alpha$ and $\beta$.

Considering the two different cases for both $\alpha$ and $\beta$, I find:

For a: if +, then $\alpha=\frac{\omega}{c}$. If -, $\alpha=0$

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

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