Modulational instability in nonlinear nonlocal equations of regularized long wave type

PHYSICA D-NONLINEAR PHENOMENA

卷:325

Article

Hur, Vera Mikyoung¹  Pandey, Ashish Kumar¹ 

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

关键词: Modulational instability;    Nonlinear nonlocal;    Regularized long wave;    BBM;    Boussinesq;    Fractional dispersion;   

DOI  :  10.1016/j.physd.2016.03.005

来源: Elsevier

【 摘 要 】

We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin-Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations. Published by Elsevier B.V.

【 授权许可】

Free