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The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…

Exactly Solvable and Integrable Systems · Physics 2020-11-20 Juncai Pu , Jun Li , Yong Chen

A rogue wave formation mechanism is proposed within the framework of a coupled nonlinear Schrodinger (CNLS) system corresponding to the interaction of two waves propagating in oblique directions in deep water. A rogue condition is…

Pattern Formation and Solitons · Physics 2015-06-22 Mark J. Ablowitz , Theodoros P. Horikis

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the…

Pattern Formation and Solitons · Physics 2017-10-06 Li-Chen Zhao , Liang Duan , Peng Gao , Zhan-Ying Yang

We study fundamental rogue-wave solutions of the focusing nonlinear Schr\"odinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)$ are proportional to the order (the far-field limit). We…

Exactly Solvable and Integrable Systems · Physics 2021-03-02 Deniz Bilman , Peter D. Miller

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear…

Optics · Physics 2013-07-17 Yu. V. Bludov , R. Driben , V. V. Konotop , B. A. Malomed

We study on the relations between modulational instability and several well-known nonlinear excitations in a nonlinear fiber, such as bright soliton, nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and Kuznetsov-Ma…

Pattern Formation and Solitons · Physics 2016-04-08 Li-Chen Zhao , Liming Ling

The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…

Fluid Dynamics · Physics 2015-11-03 Y. Charles Li

General rogue waves in the Davey-Stewartson-II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the…

Exactly Solvable and Integrable Systems · Physics 2015-06-12 Yasuhiro Ohta , Jianke Yang

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 construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…

Exactly Solvable and Integrable Systems · Physics 2014-07-14 K. Manikandan , M. Senthilvelan

We investigate a higher order nonlinear Schr\"odinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we…

Pattern Formation and Solitons · Physics 2023-10-17 A. Calini , C. L. Ellisor , C. M. Schober , E. Smith

We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…

Pattern Formation and Solitons · Physics 2021-08-31 N. Sinthuja , K. Manikandan , M. Senthilvelan

We predict the existence of linear discrete rogue waves governed by the discrete nonlinear Schrodinger equation. We discuss that Josephson effect is the underlying reason for the formation of such waves.

Optics · Physics 2020-01-08 C. Yuce

We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…

Chaotic Dynamics · Physics 2013-05-15 Miguel Onorato , Davide Proment

We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose-Einstein condensates with Raman-induced spin-orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions…

Quantum Gases · Physics 2024-09-16 Jun-Tao He , Hui-Jun Li , Ji Lin , Boris A. Malomed

The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…

Pattern Formation and Solitons · Physics 2009-08-21 E. Arevalo

Rogue waves, characterized by their abrupt and extreme localization in space and time, have evolved from maritime folklore to subjects of intense study across diverse fields, from hydrodynamics and nonlinear optics to plasmas and condensed…

Pattern Formation and Solitons · Physics 2026-05-19 Yasuhiro Miyazawa , Christopher Chong , Panayotis G. Kevrekidis , Jinkyu Yang

The observation of a wave group persisting for more than 200 periods in the direct numerical simulation of nonlinear unidirectional irregular water waves in deep water is discussed. The simulation conditions are characterized by parameters…

Pattern Formation and Solitons · Physics 2021-03-31 Alexey Slunyaev

Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…

Chaotic Dynamics · Physics 2015-05-13 A. Grönlund , B. Eliasson , M. Marklund

The nonlinear Schroedinger equation possesses three distinct six-parameter families of complex-valued quasi-periodic travelling waves, one in the defocusing case and two in the focusing case. All these solutions have the property that their…

Analysis of PDEs · Mathematics 2007-05-23 Thierry Gallay , Mariana Haragus