Related papers: Rogue wave patterns associated with Okamoto polyno…
We show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center.…
In this paper, we study the general rogue wave solutions and their patterns in the vector (or $M$-component) nonlinear Schr\"{o}dinger (NLS) equation. By applying the Kadomtsev-Petviashvili hierarchy reduction method, we derived an explicit…
Rogue wave patterns in the nonlinear Schr\"{o}dinger (NLS) equation and the derivative NLS equation are analytically studied. It is shown that when the free parameters in the analytical expressions of these rogue waves are large, these…
Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…
We report new rogue wave patterns in the nonlinear Schr\"{o}dinger equation. These patterns include heart-shaped structures, fan-shaped sectors, and many others, that are formed by individual Peregrine waves. They appear when multiple…
In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…
In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and their modified…
In this work, we explore the rogue wave patterns in the coupled Fokas-Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters is large enough, the general high-order rogue wave solutions…
We report rogue-wave and lump patterns associated with Umemura polynomials, which arise in rational solutions of the third Painlev\'{e} equation. We first show that in many integrable equations such as the nonlinear Schr\"odinger equation…
Rogue patterns associated with multiple roots of Adler--Moser polynomials under general multiple large parameters are studied in integrable systems. It is first shown that the multiplicity of any multiple root in any Adler--Moser polynomial…
We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system…
In this paper, novel rogue wave patterns in the nolocal nonlinear Schr\"odinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple…
The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…
General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of…
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…
This paper numerically investigates the statistical properties of rogue waves and their generation mechanisms in integrable turbulence, taking the Gerdjikov-Ivanov (GI) equation as the research object. The eigenvalue spectra of the…
We present a statistical analysis based on the height and return time probabilities of high amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational/semirational solutions, associated with…
We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schr\"{o}dinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and…
Exact explicit rational solutions of two- and one- dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional…