Statistical approach of modulational instability in the class of nonlocal NLS equation involving nonlinear Kerr-like responses with non-locality: Exact and approximated solutions

Kenmogné, Fabien; Mono, Jean Aimé; Noah, Pierre Marcel Anicet; Simo, Hervé; Dongmo, Eric-Donald; Enyegue, Timothé Thierry Odi; Donkeng, Hatou-Yvelin; Ebanda, Fabien Betené

doi:10.1016/j.wavemoti.2022.102997

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…WhereDis a nonlocality parameter and positive, giving the width of the distribution of the wave [49,52,53].…”

Section: Statistical Approachmentioning

confidence: 99%

Gravity waves’ modulational instability under the effect of drag coefficient in the ocean

Augustin,

César

2023

Phys. Scr.

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The research on oceanic gravity waves interacting with a drag coefficient has drawn a lot of attention. The interaction of these waves with a drag coefficient was recently found to be significant when modeling the propagation of these gravity waves. In this framework, the configuration involving the drag coefficient is of special interest. The gravity wave considered here is chosen to be unstable to two kinds (amplitude and phase) of perturbations. Given the complexity of the process to be investigated, it is necessary for us to make use of Miles’ theory in order to better model the evolution of these gravity waves propagating in deep water under the effect of drag coefficient, using the deterministic approach (well-known as the Benjamin–Feir method), and the statistical approach (also known as Klimontovich’s statistical average method) which is used starting from the Wigner Moyal transform. This study is performed to contribute to the understanding of the drag coefficient to the amplitudes (or phases) modulations of the driven waves: modulations that can sometimes accidentally trigger unpredictable extreme gravity waves.

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“…WhereDis a nonlocality parameter and positive, giving the width of the distribution of the wave [49,52,53].…”

Section: Statistical Approachmentioning

confidence: 99%

Gravity waves’ modulational instability under the effect of drag coefficient in the ocean

Augustin,

César

2023

Phys. Scr.

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“…However, it is very difficult to construct an appropriate Lyapunov function for system (1), because it is nonlinear and takes input control as well as random factors into account. Motivated by the above discussions and some studies in the literature [29,30], we aim to design the controller u i to ensure that system (1) satisfies the following two points:…”

Section: Introductionmentioning

confidence: 99%

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

Kang

Gao²

2022

Mathematics

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This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of the Lyapunov method and stochastic analysis skills, some novel sufficient conditions guaranteeing the stochastic stability for SCKOs are provided by constructing a new and suitable Lyapunov function for SCKOs. Finally, a numerical example is given to illustrate the effectiveness and applicability of the theoretical result.

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Stability of modulated signals in the damped mechanical network of discontinuous coupled system oscillators with irrational nonlinearities

et al. 2022

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Statistical approach of modulational instability in the class of nonlocal NLS equation involving nonlinear Kerr-like responses with non-locality: Exact and approximated solutions

Cited by 6 publications

References 32 publications

Gravity waves’ modulational instability under the effect of drag coefficient in the ocean

Gravity waves’ modulational instability under the effect of drag coefficient in the ocean

Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

Stability of modulated signals in the damped mechanical network of discontinuous coupled system oscillators with irrational nonlinearities

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