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Numerical simulations in the regime of marginal stability are described. Soliton families supported by this new model were investigated very recently 84, and there remains to derive and explore a similar 2D discrete equation. Schrodingers model shows the electrons moving around the nucleus in wave-like motions called 'orbitals'. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Bohrs model shows the electrons moving around the nucleus as circular 'orbits'. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. A nonstationary model that relies on the spatial nonlinear Schrdinger (NLS) equation with the time-dependent refractive index describes laser beams in. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability.
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Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity.