Spectral stability of wave trains in the Kawahara equation
نویسندگان
چکیده
We study the stability of spatially periodic solutions to the Kawahara equation, a fifth order, nonlinear partial differential equation. The equation models the propagation of nonlinear water-waves in the long-wavelength regime, for Weber numbers close to 1/3 where the approximate description through the Korteweg-de Vries (KdV) equation breaks down. Beyond threshold, Weber number larger than 1/3, this equation possess solitary waves just as the KdV approximation. Before threshold, true solitary waves typically do not exist. In this case, the origin is surrounded by a family of periodic solutions and only generalized solitary waves exist which are asymptotic to one of these periodic solutions at infinity. We show that these periodic solutions are spectrally stable at small amplitude. Running head: Stability of wave trains Corresponding author: Mariana Haragus, [email protected]
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