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Chapter 2

Nonlinear Dust Acoustic Rogue

Waves in a Two-Temperature

Charged Dusty Plasma

2.1 Introduction

From theoretical point of view, nonlinear rogue waves are one of the

most difficult problems in fluid dynamics [100]. These waves have been
observed in coastal waters and mid-ocean. The resulting peak may reach

the height of about 20-30 m and, by some estimates, even 60 m [121].

The rogue waves have been investigated extensively from the several as-

pects, such as in physical optics systems [122], in capillary waves [123], in
nonlinear optics [124], in optical cavities [83], in the Bose-Einstein conden-

sations [125] and in astrophysics plasmas [88, 126]. To obtain nonlinear

rogue waves in real physical systems, it is necessary to derive the cor-

responding NLS equation [127]. Moslem et al. [128] showed that the
nonlinear coupling between negative dispersion surface plasma wave and

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