Related papers: Interacting nonlinear wave envelopes and rogue wav…
Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much…
Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These…
We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the…
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the…
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…
A study of general rogue waves in some integrable reverse time nonlocal nonlinear equations is presented. Specifically, the reverse time nonlocal nonlinear Schr\"odinger (NLS) and nonlocal Davey-Stewartson (DS) equations are investigated,…
The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…
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…
We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
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…
The evolution of crossing sea states and the emergence of rogue waves in such systems are studied via numerical simulations performed using a higher order spectral method to solve the free surface Euler equations with a flat bottom. Two…
We investigate rogue wave formation and spectral downshifting in the higher-order nonlinear Schr\"odinger (HONLS) equation and its dissipative extensions: the nonlinear mean-flow damping model (NLD-HONLS) and the viscous damping model…
In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…
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…
The nonlinear Schr\"odinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear…
Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…