English
Related papers

Related papers: Universal rogue wave patterns associated with the …

200 papers

Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is…

Exactly Solvable and Integrable Systems · Physics 2025-08-05 Hans Werner Schuermann , Valery Serov

We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue…

Optics · Physics 2015-06-24 S. Efe , C. Yuce

In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…

Analysis of PDEs · Mathematics 2018-12-04 Mateusz Kluczek

The model of laminated wave turbulence presented recently unites both types of turbulent wave systems - statistical wave turbulence (introduced by Kolmogorov and brought to the present form by numerous works of Zakharov and his scientific…

Mathematical Physics · Physics 2007-05-23 E. Kartashova , A. Kartashov

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and…

Pattern Formation and Solitons · Physics 2017-03-31 Yunqing Yang , Zhenya Yan , Boris A. Malomed

There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with…

We investigate the generalized (2 + 1) Nizhnik-Novikov-Veselov equation and construct its linear eigenvalue problem in the coordinate space from the results of singularity structure analysis thereby dispelling the notion of weak Lax pair.…

Exactly Solvable and Integrable Systems · Physics 2017-09-13 P. Albares , P. G. Estevez , R. Radha , R. Saranya

In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schr\"odinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the…

Exactly Solvable and Integrable Systems · Physics 2022-07-28 N. Sinthuja , M. Senthilvelan

Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. We develop a…

Exactly Solvable and Integrable Systems · Physics 2017-04-04 Liming Ling , Li-Chen Zhao

The formation of coherent structures in noise driven phenomena and in Turbulence is a complex and fundamental question. A particulary important structure is the so-called Rogue Wave (RW) that arises as the sudden appearance of a localized…

Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four…

Exactly Solvable and Integrable Systems · Physics 2017-05-24 Xiaoen Zhang , Yong Chen , Xiaoyan Tang

We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may…

Pattern Formation and Solitons · Physics 2015-01-26 Antonio Degasperis , Stefan Wabnitz , Alejandro B. Aceves

Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a…

Exactly Solvable and Integrable Systems · Physics 2020-12-29 Yulei Cao , Peng-Yan Hu , Yi Cheng , Jingsong He

A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…

Fluid Dynamics · Physics 2007-08-01 V. P. Ruban

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…

Pattern Formation and Solitons · Physics 2019-03-27 Abhik Mukherjee , Anjan Kundu

Optical rogue waves are rare yet extreme fluctuations in the value of an optical field. The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has…

Optics · Physics 2014-10-14 John M. Dudley , Frédéric Dias , Miro Erkintalo , Goëry Genty

We construct higher order rogue wave solutions for the Gerdjikov-Ivanov equation explicitly in term of determinant expression. Dynamics of both soliton and non-soliton solutions is discussed. A family of solutions with distinct structures…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Lijuan Guo , Yongshuai Zhang , Shuwei Xu , Zhiwei wu , Jingsong He

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

In this paper we show how solutions of the Kadomtsev-Petviashvili equation may be used to explain the shape and behavior of large and rogue waves.

Mathematical Physics · Physics 2014-03-25 Mikhail Kovalyov

An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system.…

Exactly Solvable and Integrable Systems · Physics 2017-03-31 Xiao-Yong Wen , Zhenya Yan , Boris A. Malomed