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We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a…

Pattern Formation and Solitons · Physics 2015-01-26 Li-Chen Zhao , Jie Liu

We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the…

Analysis of PDEs · Mathematics 2010-04-22 Rémi Carles , Eric Dumas , Christof Sparber

It is universally accepted that the cubic, nonlinear Schrodinger equation (NLS) models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves, while the Kortewegde Vries equation (KdV) models the propagation of…

Mathematical Physics · Physics 2016-10-23 Chuangye Liu , Nghiem V. Nguyen

We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the non-linear Schrodinger equation in the Madelung…

Computational Physics · Physics 2016-11-09 Philip Mocz , Sauro Succi

We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schr\"odinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an…

Analysis of PDEs · Mathematics 2022-01-11 Van Duong Dinh

We investigate rogue wave formation and spectral downshifting in the higher-order nonlinear Schr\"odinger (HONLS) equation and its dissipative extensions: the nonlinear mean-flow damping model (NLD-HONLS) and the viscous damping model…

Pattern Formation and Solitons · Physics 2025-10-31 C. M. Schober , A. Islas

Nonlinear excitations of nuclear density are considered in the framework of semiclassical nonlinear nuclear hydrodynamics. Possible types of stationary nonlinear waves in nuclear media are analysed using Nonlinear Schroedinger equation of…

Nuclear Theory · Physics 2009-10-31 V. G. Kartavenko , A. Sandulescu , W. Greiner

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a…

Pattern Formation and Solitons · Physics 2024-05-21 T. Congy , G. A. El , G. Roberti , A. Tovbis , S. Randoux , P. Suret

The nonlinear Schr\"odinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the…

Pattern Formation and Solitons · Physics 2019-05-01 T. Congy , G. A. El , M. A. Hoefer , M. Shearer

We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields…

Pattern Formation and Solitons · Physics 2021-09-21 Mark J. Ablowitz , Justin T. Cole , Igor Rumanov

Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to…

Atmospheric and Oceanic Physics · Physics 2009-11-13 F. Dias , A. I. Dyachenko , V. E. Zakharov

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an…

Optics · Physics 2020-09-02 Giulia Marcucci , Davide Pierangeli , Claudio Conti

We demonstrate experimentally multi-bound-soliton solutions of the Nonlinear Schr\"odinger equation (NLS) in the context of surface gravity waves. In particular, the Satsuma-Yajima N-soliton solution with N=2,3,4 is investigated in detail.…

Fluid Dynamics · Physics 2013-08-09 A. Chabchoub , N. Hoffmann , M. Onorato , G. Genty , J. M. Dudley , N. Akhmediev

Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…

Exactly Solvable and Integrable Systems · Physics 2023-09-01 Solomon Manukure , Morgan McAnally , Yuan Zhou , Demetrius Rowland , Gina Pantano

The mixed nonlinear Schr\"odinger (MNLS) equation is a model for the propagation of the Alfv\'en wave in plasmas and the ultrashort light pulse in optical fibers with two nonlinear effects of self-steepening and self phase-modulation(SPM),…

Exactly Solvable and Integrable Systems · Physics 2014-07-28 Jingsong He , Shuwei Xu , Yi Cheng

The dynamics of single carrier wavepackets in nonlinear wave problems over periodic structures can be often formally approximated by the constant coefficient nonlinear Schr\"odinger equation (NLS) as an effective model for the wavepacket…

Analysis of PDEs · Mathematics 2018-09-20 Tomáš Dohnal , Daniel Rudolf

In this brief report we study numerically the spontaneous emergence of rogue waves in (i) modulationally unstable plane wave at its long-time statistically stationary state and (ii) bound-state multi-soliton solutions representing the…

Pattern Formation and Solitons · Physics 2022-12-09 D. S. Agafontsev , A. A. Gelash

The cubic nonlinear Schrodinger equation (NLS) in one dimension is considered in the presence of an intensity-dependent dispersion term. We study bright solitary waves with smooth profiles which extend from the limit where the dependence of…

Pattern Formation and Solitons · Physics 2024-08-22 P. G. Kevrekidis , D. E. Pelinovsky , R. M. Ross

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002, 2014]]: for…

Fluid Dynamics · Physics 2023-10-12 A. V. Slunyaev , V. I. Shrira

Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…

Pattern Formation and Solitons · Physics 2015-12-04 Evgeny M. Gromov , Boris A. Malomed