# Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons

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## Abstract

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## 1. Introduction

## 2. Governing Equations

## 3. Derivation of the NLSE

## 4. Modulational Instability and Rogue Waves

## 5. Results and Discussion

## 6. Conclusions

- Fast and slow DIA modes have been observed.
- Both modulationally stable (i.e., $P/Q<0$) and unstable (i.e., $P/Q>0$) parametric regimes of the DIAWs can exist for both fast and slow modes.
- The amplitude of the first and second-order DIARWs decreases (increases) with ion (electron) temperature.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The variation of ${\omega}_{f}$ vs. k (

**left panel**) and ${\omega}_{s}$ vs. k (

**right panel**) when other plasma parameters are $\kappa =1.8$, $\rho =1\times {10}^{3}$, $\mu =3\times {10}^{-6}$, ${\mu}_{2}=0.3$, and ${\mu}_{3}=0.05$.

**Figure 2.**The variation of $P/Q$ with k for different values of $\kappa $ for $\omega \equiv {\omega}_{f}$ (

**left panel**) and $\omega \equiv {\omega}_{s}$ (

**right panel**) when other plasma parameters are $\rho =1\times {10}^{3}$, $\mu =3\times {10}^{-6}$, ${\mu}_{2}=0.3$, and ${\mu}_{3}=0.05$.

**Figure 3.**The variation of ${\mathsf{\Gamma}}_{g}$ with $\tilde{k}$ for different values of ${\mu}_{3}$ (

**left panel**) and the variation of $|{\Phi}_{1}|$ with $\xi $ for different values of ${\mu}_{2}$ (

**right panel**) when other plasma parameters are $k=1.3$, ${\tilde{\Phi}}_{0}=0.5$, $\kappa =1.8$, $\rho =1\times {10}^{3}$, $\mu =3\times {10}^{-6}$, and $\omega \equiv {\omega}_{f}$.

**Figure 4.**The variation of $|{\Phi}_{2}|$ with $\xi $ for different values of ${\mu}_{2}$ (

**left panel**) and the comparison between the first-order (dashed green curve) and second-order (solid blue curve) rational solutions of NLSE (

**right panel**) when other plasma parameters are $\tau =0$, $k=1.3$, ${\tilde{\Phi}}_{0}=0.5$, $\kappa =1.8$, $\rho =1\times {10}^{3}$, $\mu =3\times {10}^{-6}$, ${\mu}_{3}=0.05$, and $\omega \equiv {\omega}_{f}$.

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**MDPI and ACS Style**

Noman, A.A.; Islam, M.K.; Hassan, M.; Banik, S.; Chowdhury, N.A.; Mannan, A.; Mamun, A.A.
Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons. *Gases* **2021**, *1*, 106-116.
https://doi.org/10.3390/gases1020009

**AMA Style**

Noman AA, Islam MK, Hassan M, Banik S, Chowdhury NA, Mannan A, Mamun AA.
Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons. *Gases*. 2021; 1(2):106-116.
https://doi.org/10.3390/gases1020009

**Chicago/Turabian Style**

Noman, Akib Al, Md Khairul Islam, Mehedi Hassan, Subrata Banik, Nure Alam Chowdhury, Abdul Mannan, and A. A. Mamun.
2021. "Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons" *Gases* 1, no. 2: 106-116.
https://doi.org/10.3390/gases1020009