In this paper, we consider the integrable extended complex modified Korteweg–de Vries equation. Based on Darboux transformation, obtain soliton molecules, positon solutions, rational solutions and rogue waves for Further, under standard decomposition, divide into three patterns: fundamental pattern, triangular pattern ring pattern. On basis of define length width discuss effect different parame...

Abstract. Very steep waves constitute an essentially nonlinear and complicated phenomenon. Inter-related experimental and theoretical efforts are thus required to gain a better understanding of their generation and propagation mechanisms. A nonlinear focusing process in which a single unidirectional steep wave emerges from an initially wide amplitudeand frequency-modulated wave group at a predi...

A substantial part of the energy of wake waves from high-speed ships sailing in shallow water is concentrated in nonlinear components which at times have a solitonic nature. Recent results of investigations into solitonic wave interactions within the framework of the Kadomtsev-Petviashvili equation and their implications for rogue wave theory are reviewed. A surface elevation four times as high...

We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrödinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynami...

A new model of pump noise in supercontinuum and rogue wave generation is presented. Simulations are compared with experiments and show that the new model provides significantly better agreement than the currently ubiquitously used one-photon-per-mode model. The new model also allows for a study of the influence of the pump spectral line width on the spectral broadening mechanisms. Specifically,...

Directional wave energy focusing in space is one of the mechanisms that may contribute to the generation of a rogue wave in the ocean. To this effect, in this paper, we study the generation of extreme waves in a three-dimensional numerical wave tank from the motion of a snake wavemaker. The numerical model solves incompressible fully nonlinear free-surface Euler equations for potential flow, us...

Stochastic numerical simulations are used to study the statistical properties of supercontinuum spectra generated in photonic crystal fibre with two zero dispersion wavelengths. For picosecond pulse excitation, we examine how the statistical properties of solitons generated on the long wavelength edge of the supercontinuum (“optical rogue waves”) are modified by energy transfer to dispersive wa...

We study the properties of the chaotic wave fields generated in the frame of the SasaSatsuma equation when a plane wave solution is randomly perturbed with a white noise. We have found that plane waves with different propagation constant splits into selffocused filaments, that propagate with a velocity which is well approximately given by the group velocity calculated from the dispersion relati...

Internal waves in a stratified fluid with constant buoyancy frequency were studied, special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue for triads general physical setting have recently been derived analytically, but the implications mechanics context not yet fully assessed. Numerical simulations conducted cas...