The Regularized Boussinesq equation: Instability of periodic traveling waves
نویسندگان
چکیده
منابع مشابه
Linear Stability Analysis for Periodic Traveling Waves of the Boussinesq Equation and the Kgz System
The question for linear stability of spatially periodic waves for the Boussinesq equation (the cases p = 2, 3) and the Klein-Gordon-Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their linear stability (instability respectively), when the perturbations are taken with the same period T . In particular, our results allow us to completely re...
متن کاملTraveling waves of the regularized short pulse equation
The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by ...
متن کاملTransverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev-Petviashvili Equation
In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev-Petviashvili equation. By analyzing high and low frequency limits of the appropriate periodic Evans function, we derive an orientation index which yields sufficient conditions for such a...
متن کاملOn the Instability of a Class of Periodic Travelling Wave Solutions of the Modified Boussinesq Equation
This paper is concerned with instability of periodic travelling wave solutions of the modified Boussinesq equation. Periodic travelling wave solutions with a fixed fundamental period Lwill be constructed by using Jacobi’s elliptic functions. It will be shown that these solutions, called dnoidal waves, are nonlinearly unstable in the energy space for a range of their speeds of propagation and pe...
متن کاملInstability of Periodic Sign-changed Waves for Sine-gordon Equation
The present paper deals with results of orbital instability of periodic waves related to sine-Gordon equation. Our periodic solutions obtained in our study tend to a kink wave solutions in the infinite wavelength scenario. The approaches used here will be the classical Grillakis, Shatah and Strauss’ theory.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2013
ISSN: 0022-0396
DOI: 10.1016/j.jde.2013.01.034