Direct dynamical energy cascade in the modified KdV equation

Denys Dutykh, Elena Tobisch

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageBritish English
Pages (from-to)76-87
Number of pages12
JournalPhysica D: Nonlinear Phenomena
StatePublished - 15 Mar 2015


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


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