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Regular version of the site

Article

Conditions for modulation instability in higher order Korteweg-de Vries equations

Applied Mathematics Letters. 2019. Vol. 88. P. 28-32.
Tobisch E., Pelinovsky E.

The universal mechanism of modulation instability (MI) has been discovered first for the Nonlinear
Schr¨odinger equation (NLS) and is well studied in the frame of the higher order NLS equations.
Recent studies demonstrated by pure existence theorems that also the higher order Korteweg-de
Vries (KdV) equations might possess the MI. In this Letter we present explicit form of the conditions
for the MI to appear in the KdV-family of equations of the general form ut + sup ux + uxxx =0 
where s = ±1 with p > 0 being an arbitrary integer.