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The one-dimensional focusing nonlinear Schrodinger equation (NLSE) on an unstable condensate background is the fundamental physical model, that can be applied to study the development of modulation instability (MI) and formation of rogue…

Exactly Solvable and Integrable Systems · Physics 2018-02-14 A. A. Gelash

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the Rogue waves are localized surface waves, their theoretical models and experimental…

Exactly Solvable and Integrable Systems · Physics 2015-03-13 Anjan Kundu , Abhik Mukherjee , Tapan Naskar

In this work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require…

Pattern Formation and Solitons · Physics 2017-03-14 Michelle D. Maiden , Mark. A. Hoefer

In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…

Plasma Physics · Physics 2008-09-12 Vikrant Saxena , Amita Das , Sudip Sengupta , Predhiman Kaw , Abhijit Sen

We consider the propagation of temporally incoherent waves in multimode optical fibers (MMFs) in the framework of the multimode nonlinear Schr\"odinger (NLS) equation accounting for the impact of the natural structural disorder that affects…

Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model,…

Plasma Physics · Physics 2013-05-16 B. Friedman , T. A. Carter , M. V. Umansky , D. Schaffner , I. Joseph

We demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state (NESS) with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures.…

Fluid Dynamics · Physics 2025-08-15 Nadia Bihari Padhan , Dario Vincenzi , Rahul Pandit

Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model's differential rotation yields stability in the absence of a magnetic field, but if a…

Plasma Physics · Physics 2019-02-19 Abigail Plummer , J. B. Marston , S. M. Tobias

By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskiiequation including the current nonlinearity. The analysis shows that this nonlinearity partly…

Quantum Gases · Physics 2021-03-24 Ishfaq Ahmad Bhat , S. Sivaprakasam , Boris A. Malomed

We consider the cubic nonlinear Schr\"odinger (NLS) equation with a linear damping on the one dimensional torus and we investigate the stability of some solitary wave profiles within the dissipative dynamics. The undamped cubic NLS equation…

Analysis of PDEs · Mathematics 2025-02-28 Paolo Antonelli , Boris Shakarov

In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidimensional (generalizations of the focusing) nonlinear…

Pattern Formation and Solitons · Physics 2026-05-27 Francesco Coppini , Paolo Maria Santini

The modulational instability of waves in a medium under the action of an external monochromatic force and dissipation is considered. The model which describes the nonlinear stage of the modulation instability was constructed with using…

Pattern Formation and Solitons · Physics 2012-11-29 Evgeny Belkin , Alexander Kirichok , Vladimir Kuklin

We study a one-dimensional discrete nonlinear Schr\"odinger model with hopping to the first and a selected N-th neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability…

Quantum Gases · Physics 2016-06-10 J. Stockhofe , P. Schmelcher

We measure evolution of spectra, spatial correlation functions and probability density functions (PDFs) of waves appearance for a set of one-dimensional NLS-like equations of focusing type, namely for the classical integrable Nonlinear…

Optics · Physics 2015-03-20 Dmitry Agafontsev , Vladimir Zakharov

We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…

Exactly Solvable and Integrable Systems · Physics 2015-08-24 Alexis Arnaudon

The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and…

Pattern Formation and Solitons · Physics 2012-01-04 I. V. Barashenkov , M. A. Molchan

The focusing NLS equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, considered the main physical mechanism for the appearance of rogue (anomalous)…

Exactly Solvable and Integrable Systems · Physics 2017-08-15 P. G. Grinevich , P. M. Santini

Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a…

Fluid Dynamics · Physics 2022-12-16 Pavan V. Kashyap , Yohann Duguet , Olivier Dauchot

We consider the instability and stability of periodic stationary solutions to the classical \phi^4 equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and…

Pattern Formation and Solitons · Physics 2023-04-05 Meng-Meng Liu , Wen-Rong Sun , Lei Liu , P. G. Kevrekidis , Lei Wang

Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons…

Fluid Dynamics · Physics 2023-10-10 Marcelo V. Flamarion , Efim Pelinovsky , Ekaterina Didenkulova