| Abstract: |
| Nonlinear waves in dispersive media can be succeptible to modulational insta-
bilities. We examine a category of scalar equations, with general dispersion and monomial
nonlinearity, including a large variety of KdV-like equations. For small-amplitude traveling
wave solutions, we provide a complete characterization of the spectrum near the origin of
the linear operator obtained from linearizing about periodic traveling waves. We prove rig-
orously that, when the modulational instability is present, the spectrum connected to the
origin consists of curves that invariably form a closed figure-eight pattern. |
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