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Regular version of the site

Article

Constructive study of modulation instability in higher order Korteweg-de Vries equations

Fluids, Basel, Switzerland. 2019. Vol. 4. No. 54. P. 1-13.
Tobisch E., Pelinovsky E.

Our present study is devoted to the constructive study of the modulational instability
for the Korteweg-de Vries (KdV)-family of equations ut + sup ux + uxxx (here s = 1 and p > 0 is
an arbitrary integer). For deducing the conditions of the instability, we first computed the nonlinear
corrections to the frequency of the Stokes wave and then explored the coefficients of the corresponding
modified nonlinear Schrödinger equations, thus deducing explicit expressions for the instability
growth rate, maximum of the increment and the boundaries of the instability interval. A brief
discussion of the results, open questions and further research directions completes the paper.