# Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma

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## Abstract

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## 1. Introduction

## 2. Governing Equations

## 3. Derivation of the NLSE

## 4. Modulational Instability and Envelope Solitons

## 5. Numerical Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The bright (left panel) and dark (right panel) envelope solitons for $k=1.6$ and $k=1.2$, respectively, along with $\eta =0.07$, $\rho =1.2$, $\varrho =1.5$, $\kappa =2$, ${\mu}_{1}=0.8$, ${\mu}_{2}=0.3$, $\tau =0$, ${\psi}_{0}=0.0005$, $U=0.2$, and ${\mathsf{\Omega}}_{0}=0.4$.

**Figure 2.**Plot of $P/Q$ vs. k for the change of $\eta $ (left panel) and ${\mu}_{1}$ (right panel) when $\rho =1.2$, $\varrho =1.5$, $\kappa =2$, and ${\mu}_{2}=0.5$.

**Figure 3.**Plot of $P/Q$ vs. k for the change of $\rho $ (left panel) and $\kappa $ (right panel) when $\eta =0.07$, $\varrho =1.5$, ${\mu}_{1}=0.7$, and ${\mu}_{2}=0.5$.

R (${\mathit{R}}_{\mathit{s}}$) | ${\mathit{T}}_{\mathit{e}2}$ (eV) | ${\mathit{T}}_{\mathit{e}1}$ (eV) | ${\mathit{n}}_{\mathit{e}2}$ (cm^{−3}) | ${\mathit{n}}_{\mathit{e}1}$ (cm^{−3}) |
---|---|---|---|---|

5.40 | 1.8 | 300 | 10.5 | 0.02 |

6.30 | 2.0 | 400 | 10.5 | 0.01 |

9.80 | 8.0 | 1100 | 2.5 | 0.07 |

12.0 | 6.0 | 1200 | 1.0 | 0.11 |

13.1 | 10.2 | 1000 | 0.21 | 0.18 |

14.0 | 30 | 900 | 0.15 | 0.10 |

15.2 | 70 | 900 | 0.25 | 0.10 |

17.8 | 28 | 1000 | 0.15 | 0.07 |

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**MDPI and ACS Style**

Banik, S.; Heera, N.M.; Yeashna, T.; Hassan, M.R.; Shikha, R.K.; Chowdhury, N.A.; Mannan, A.; Mamun, A.A.
Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma. *Gases* **2021**, *1*, 148-155.
https://doi.org/10.3390/gases1030012

**AMA Style**

Banik S, Heera NM, Yeashna T, Hassan MR, Shikha RK, Chowdhury NA, Mannan A, Mamun AA.
Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma. *Gases*. 2021; 1(3):148-155.
https://doi.org/10.3390/gases1030012

**Chicago/Turabian Style**

Banik, Subrata, Nadiya Mehzabeen Heera, Tasfia Yeashna, Md. Rakib Hassan, Rubaiya Khondoker Shikha, Nure Alam Chowdhury, Abdul Mannan, and A A Mamun.
2021. "Modulational Instability of Ion-Acoustic Waves and Associated Envelope Solitons in a Multi-Component Plasma" *Gases* 1, no. 3: 148-155.
https://doi.org/10.3390/gases1030012