Constructive Study of Modulational Instability in Higher Order Korteweg-de Vries Equations
Institute of Analysis, Johannes Kepler University Linz, 4040 Linz, Austria
National Research University—Higher School of Economics, Moscow 101000, Russia
Institute of Applied Physics, Russian Academy of Sciences, Nizhni Novgorod 603950, Russia
Nizhni Novgorod State Technical University n.a. R.Y. Alexeev, Nizhni Novgorod 603155, Russia
Author to whom correspondence should be addressed.
Received: 2 February 2019 / Revised: 4 March 2019 / Accepted: 12 March 2019 / Published: 17 March 2019
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Our present study is devoted to the constructive study of the modulational instability for the Korteweg-de Vries (KdV)-family of equations
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.
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Tobisch, E.; Pelinovsky, E. Constructive Study of Modulational Instability in Higher Order Korteweg-de Vries Equations. Fluids 2019, 4, 54.
Tobisch E, Pelinovsky E. Constructive Study of Modulational Instability in Higher Order Korteweg-de Vries Equations. Fluids. 2019; 4(1):54.
Tobisch, Elena; Pelinovsky, Efim. 2019. "Constructive Study of Modulational Instability in Higher Order Korteweg-de Vries Equations." Fluids 4, no. 1: 54.
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