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We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which possess complicated wave propagations in time and are…

Exactly Solvable and Integrable Systems · Physics 2011-05-19 Zhenya Yan , Dongmei Jiang , W. M. Liu

Under investigation in this work is the robust inverse scattering transform of the discrete Hirota equation with nonzero boundary conditions, which is applied to solve simultaneously arbitrary-order poles on the branch points and spectral…

Mathematical Physics · Physics 2023-11-21 Guixian Wang , Xiu-Bin Wang , Bo Han

We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…

Analysis of PDEs · Mathematics 2020-02-19 Thies Gerken

Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow…

Fluid Dynamics · Physics 2025-02-07 Saulo Mendes , Yuchen He , Jérôme Kasparian , Amin Chabchoub

We discuss the possible advantages of using the wavelet transform over the Fourier transform for the early detection of rogue waves. We show that the triangular wavelet spectra of the rogue waves can be detected at early stages of the…

Fluid Dynamics · Physics 2015-12-09 Cihan Bayindir

This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schr\"odinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW…

Exactly Solvable and Integrable Systems · Physics 2026-04-30 Zixuan Deng , Huian Lin , Liming Ling

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with…

General Mathematics · Mathematics 2023-06-07 H. C. Rosu , S. C. Mancas

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

The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather…

Exactly Solvable and Integrable Systems · Physics 2022-06-08 Bao-Feng Feng , Liming Ling

Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe propagation of nonlinear and dispersive water waves of significant interest such as solitary and tsunami waves. The initial-boundary value problem on a…

Analysis of PDEs · Mathematics 2022-10-10 Dionyssios Mantzavinos , Dimitrios Mitsotakis

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 consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to…

Pattern Formation and Solitons · Physics 2024-01-23 Wen-Rong Sun , Boris A. Malomed , Jin-Hua Li

We show that monochromatic long-crested corrugations on an otherwise flat seafloor can coherently scatter the energy of an oblique incident internal wave to multiple multi-directional higher-mode waves via a series of resonant interactions.…

Fluid Dynamics · Physics 2017-11-22 Louis-Alexandre Couston , Yong Liang , Mohammad-Reza Alam

We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…

Pattern Formation and Solitons · Physics 2014-07-15 Li-Chen Zhao , Chong Liu , Zhan-ying Yang

In this paper we analyze the rogue wave spectra of the Kundu-Eckhaus equation (KEE). We compare our findings with their nonlinear Schrodinger equation (NLSE) analogs and show that the spectra of the individual rogue waves significantly…

Pattern Formation and Solitons · Physics 2016-06-22 Cihan A. Bayindir

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE.…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 Chengshi Liu

In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condensates. These waveforms lead to significantly and controllably…

Pattern Formation and Solitons · Physics 2025-02-21 Jimmie Adriazola , Panayotis Kevrekidis

We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…

Exactly Solvable and Integrable Systems · Physics 2019-10-15 Bao-Feng Feng , Liming Ling , Daisuke A. Takahashi

We demonstrate a way to generate a two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in model of a broad-area surface-emitting laser…

Pattern Formation and Solitons · Physics 2017-03-08 Mustapha Tlidi , Krassimir Panajotov

This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…

Analysis of PDEs · Mathematics 2024-08-13 Deniz Bilman , Peter D. Miller