Related papers: Rogue waves and their patterns for the coupled Fok…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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.…
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…
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…
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…
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…