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Related papers: On the nonlinear stage of Modulation Instability

200 papers

In the framework of Gurevich and Pitaevskii approach [1] we construct modulated by Whitham [2] solution of nonlinear Shrodinger (NS) equation partially saturating the modulational instability. This solution describes new scenario of…

patt-sol · Physics 2008-02-03 Ramil' F. Bikbaev , Vadim R. Kudashev

We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schr\"odinger equation (NLSE) with competing cubic-quintic nonlinearities and the L\'evy index (fractionality) taking values 1…

Pattern Formation and Solitons · Physics 2020-04-01 Pengfei Li , Boris A. Malomed , Dumitru Mihalache

We study pattern-forming nonlinear dynamics starting from a continuous wave state of quasi-one-dimensional two-component Bose-Einstein condensates with synthetic spin-orbit coupling induced by Raman lasers. Modulation instability can occur…

Quantum Gases · Physics 2019-02-20 Thudiyangal Mithun , Kenichi Kasamatsu

A three-component nonlinear Schrodinger-type model which describes spinor Bose-Einstein condensate (BEC) is considered. This model is integrable by the inverse scattering method and using Zakharov-Shabat dressing method we obtain three…

Exactly Solvable and Integrable Systems · Physics 2009-07-30 V. A. Atanasov , V. S. Gerdjikov , G. G. Grahovski , N. A. Kostov

Static soliton bound states in nonlinear systems are investigated analytically and numerically in the framework of the parametrically driven, damped nonlinear Schr\"odinger equation. We find that the ordinary differential equations, which…

Pattern Formation and Solitons · Physics 2024-05-14 M. M. Bogdan , O. V. Charkina

The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schr\"{o}dinger equations mainly the compactness of the support and its spatial localization. This question is very related with pure…

Analysis of PDEs · Mathematics 2015-03-17 Pascal Bégout , Jesús Ildefonso Díaz

The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices,…

Other Condensed Matter · Physics 2009-11-10 L. D. Carr , Charles W. Clark

We introduce a system of two linearly coupled discrete nonlinear Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose-Einstein condensates (BEC).…

Pattern Formation and Solitons · Physics 2010-11-23 H. Susanto , P. G. Kevrekidis , F. Kh. Abdullaev , Boris A. Malomed

A method for approximating dark soliton solutions of the nonlinear Schrodinger equation under the influence of perturbations is presented. The problem is broken into an inner region, where core of the soliton resides, and an outer region,…

Mathematical Physics · Physics 2015-05-19 Mark J. Ablowitz , Sean D. Nixon , Theodoros P. Horikis , Dimitri J. Frantzeskakis

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…

Pattern Formation and Solitons · Physics 2013-11-28 R. K. Jackson , R. Marangell , H. Susanto

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schr\"odinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the…

Other Condensed Matter · Physics 2015-06-25 Fatkhulla Kh. Abdullaev , Josselin Garnier

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

The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…

General Relativity and Quantum Cosmology · Physics 2021-09-22 Riccardo Falcone , Daniela D. Doneva , Kostas D. Kokkotas , Stoytcho S. Yazadjiev

A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is…

Plasma Physics · Physics 2015-05-27 Dian Zhao , M. Y. Yu

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In…

Pattern Formation and Solitons · Physics 2015-01-08 David Novoa , Daniele Tommasini , José A. Nóvoa-López

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of…

Pattern Formation and Solitons · Physics 2009-11-10 Hidetsugu Sakaguchi , Boris A. Malomed

Modulation instability (MI) in continuous media described by a system of two cubic-quintic nonlinear Schr\"odinger equations (NLSE) has been investigated with a focus on revealing the contribution of the quintic nonlinearity to the…

Pattern Formation and Solitons · Physics 2018-12-26 B. B. Baizakov , A. Bouketir , S. M. Al-Marzoug , H. Bahlouli

We study the properties of modulational instability and discrete breathers arising in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Conditions for modulation instability and instability regions…

Pattern Formation and Solitons · Physics 2025-12-01 Sherzod R. Otajonov , Bakhram A. Umarov , Fatkhulla Kh. Abdullaev

We investigate exact travelling wave solutions of higher order nonlinear Schrodinger equation in the absence of third order dispersion, which exhibit non-trivial self phase modulation. It is shown that, the corresponding dynamical equation,…

Pattern Formation and Solitons · Physics 2011-06-01 Anshul Saini , Vivek M. Vyas , S. N. Pandey , T. Solomon Raju , Prasanta K. Panigrahi

The nonlinear Schr{\"o}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the…

Analysis of PDEs · Mathematics 2016-09-16 Stefan Le Coz , Yifei Wu