Direct dynamical energy cascade in the modified KdV equation

PHYSICA D-NONLINEAR PHENOMENA

卷:297

Article

Dutykh, Denys¹  Tobisch, Elena² 

[1] Univ Savoie, LAMA, UMR CNRS 5127, F-73376 Le Bourget Du Lac, France

[2] Johannes Kepler Univ Linz, Inst Anal, A-4040 Linz, Austria

关键词: Modulational instability;    Energy cascade;    Korteweg-de Vries equation;    Modified KdV equation;    NLS equation;   

DOI  :  10.1016/j.physd.2015.01.002

来源: Elsevier

【 摘 要 】

In this study we examine the energy transfer mechanism during the nonlinear stage of the Modulational Instability (MI) in the modified Korteweg-de Vries (mKdV) equation. The particularity of this study consists in considering the problem essentially in the Fourier space. A dynamical energy cascade model of this process originally proposed for the focusing NLS-type equations is transposed to the mKdV setting using the existing connections between the KdV-type and NLS-type equations. The main predictions of the D-cascade model are outlined and validated by direct numerical simulations of the mKdV equation using the pseudo-spectral methods. The nonlinear stages of the MI evolution are also investigated for the mKdV equation. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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