Abstract
Rogue waves are giant nonlinear waves that suddenly appear and disappear in oceans and optics. We discuss the facts and fictions related to their strange nature, dynamic generation, ingrained instability, and potential applications. We present rogue wave solutions to the standard cubic nonlinear Schrödinger equation that models many propagation phenomena in nonlinear optics. We propose the method of mode pruning for suppressing the modulation instability of rogue waves. We demonstrate how to produce stable Talbot carpets—recurrent images of light and plasma waves—by rogue waves, for possible use in nanolithography. We point to instances when rogue waves appear as numerical artefacts, due to an inadequate numerical treatment of modulation instability and homoclinic chaos of rogue waves. Finally, we display how statistical analysis based on different numerical procedures can lead to misleading conclusions on the nature of rogue waves.
Highlights
Analytical and numerical solutions of the nonlinear Schrödinger equation (NLSE) of different orders have been widely analyzed for their importance in a number of mathematical and physical systems [1,2,3,4,5,6,7,8,9,10,11]
We have discussed the facts and fictions related to the strange nature, dynamic generation, ingrained instability, and potential applications of rogue wave (RW)
We have proposed the method of mode pruning for suppressing the modulation instability of rogue waves
Summary
Analytical and numerical solutions of the nonlinear Schrödinger equation (NLSE) of different orders have been widely analyzed for their importance in a number of mathematical and physical systems [1,2,3,4,5,6,7,8,9,10,11]. The modulation instability can be regarded as a nonlinear optical process where the power of the fundamental pump wave is attenuated and redistributed to a finite number of spectral sidebands These higher-order modes are very weak at the onset of nonlinear evolution but their power increases exponentially during propagation [3,4,13]. It is questionable whether the chaotic behavior is intrinsic to the model equation or is induced by the numerical algorithm applied [28,29] To address this question, we revisit our previous results [32] on the analytical and numerical NLSE solutions that are periodic both along the temporal and spatial axes, known as the Talbot self-images or carpets [25,33,34].
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