Direct dynamical energy cascade in the modified KdV equation

作者：Dutykh Denys; Tobisch Elena^*

来源：Physica D: Nonlinear Phenomena , 2015, 297: 76-87.

DOI：10.1016/j.physd.2015.01.002

• Modulational instability
• Energy cascade
• Korteweg-de Vries equation
• Modified KdV equation
• NLS equation

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.

• 出版日期2015-3-15