Modulational Instability of Nonlinear Wave Packets within (2+4) Korteweg–de Vries Equation
Oksana Kurkina,
Efim Pelinovsky,
Andrey Kurkin
Affiliations
Oksana Kurkina
Department of Applied Mathematics, Nizhny Novgorod State Technical University, n.a. R.E. Alekseev, 603155 Nizhny Novgorod, Russia
Efim Pelinovsky
Nonlinear Geophysical Processes Department, Federal Research Center A.V. Gaponov-Grekhov, Institute of Applied Physics of the Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
Andrey Kurkin
Department of Applied Mathematics, Nizhny Novgorod State Technical University, n.a. R.E. Alekseev, 603155 Nizhny Novgorod, Russia
The higher-order nonlinear Schrödinger equation with combined nonlinearities is derived by an asymptotic reduction from the (2+4) Korteweg–de Vries model for weakly nonlinear wave packets for the context of interfacial waves in a three-layer symmetric media. Focusing properties and modulation instability effects are discussed for the considered physical context. Instability growth rate, maximum of the increment and the boundaries of the instability interval are derived in terms of three-layer density stratification, their structure on the parameter planes of relative layer depth, carrier wavenumber and envelope amplitude, are considered in detail.
