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the low-frequency ion acoustic perturbations can lead to propagation of

the nonlinear surface plasma rogue waves. El-Labany et al. [129] in-

spected the existence of rogue wave in a negative-positive ion plasmas in
Titan’s atmosphere. Abdelwahed and El-Shewy [130] investigated the

improvement of IAW shape in warm plasmas and explained the explosive

and rouge waves by the rational solutions of NLS equations. Furthermore,

many studies in astrophysics used the rational solutions of NLS equa-
tion that give a suitable rogue waves description [131-133]. Chawla et al.

[134] examined the effect of plasma parameters on the stability of mod-

ulation of IAWs in a collisionless (e-p-i) plasma with warm ions. They
found that, the instability regions are shifted according to the wavenum-

ber. On the other hand, El Wakil et al. [135] studied the rational solution

of the NLS equation equation in auroral zone plasma. El-Bedwehy and
Moslem [136] studied the properties of nonlinear structures of solitons

and shocks in magnetoplasma in the presence of electrons and positrons

obeying kappa distribution. Recently, Guo et al. [137] investigated rogue
waves in the case of unmagnetized plasma via the NLS equation. Based

on the dispersion and nonlinear coefficients that depend mainly on the

plasma parameters, the stability (instability) regions are also studied and

they observed rogue wave triplets in the unstable region. In this chapter,
DA rogue wave in collisionless unmagnetized dusty plasmas consisting of

electrons, nonthermal ions, hot and cold dust grains will be studied.

2.2 Basic Equations

The dusty plasma model, we are studying, is unmagnetized and consists
of four components: isothermal electrons, and nonthermal ions, hot and

cold dust species. The electrons are assumed to follow the Boltzmann

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