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Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities

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Abstract

In this paper, the modulational instability of the one-dimensional optical soliton has been studied in the presence of Gaussian and sine oscillatory nonlocal response functions. By properly managing the sign as well as the magnitude of cubic, quintic and septimal nonlinearities and the strength of nonlocal response functions, a remarkable impact on the dynamics of modulational instability has been observed. We have investigated both the symmetric (equal power values for pump and probe beams) and asymmetric (unequal power values for pump and probe beams) cases, in which the asymmetric case shows a reduced bandwidth of MI compared to the symmetric case. Furthermore, our study has revealed the emergence of both type A and type B Akhmediev breathers under specific combinations of higher-order nonlinearities and nonlocal response functions. Specifically, the Gaussian nonlocal response function leads to the formation of type A Akhmediev breathers, while the sine oscillatory nonlocal response function can give rise to both type A and type B Akhmediev breathers, which depends upon the strength of the nonlocal response function.

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Abbreviations

SPR:

Surface plasma resonance

MDNC:

Metal dielectric nanocomposite

HON:

Higher-order nonlinearity

MI:

Modulational instability

NLS:

Nonlinear Schrödinger

1D:

One-dimensional

2D:

Two-dimensional

PW:

Plane wave

GVD:

Group velocity dispersion

CW:

Continuous wave

AB:

Akhmediev breather

XPM:

Cross-phase modulation

\(q_1\) :

Amplitude of pump beam

\(q_2\) :

Amplitude of probe beam

x :

Spatial coordinate

z :

Propagation distance

\(\alpha _1\) :

Cubic nonlinearity strength

\(\alpha _2\) :

Quintic nonlinearity strength

\(\alpha _3\) :

Septimal nonlinearity strength

\(R_j(x-x^{\prime })\) :

Nonlocal response functions

\(P_1\) :

Power of pump beam

\(P_2\) :

Power of probe beam

\(b_{\zeta }\) :

Complex perturbation

\(\sigma \) :

Strength of nonlocal response functions

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Acknowledgements

JBS acknowledge Centre for Computational Modeling (CCM), Chennai Institute of Technology, Chennai 600 069, India, for providing fund via funding number CIT/CNS/2023/RP-016. EK work has been supported by the National Key R & D Program of China under Grant No. 2016YFA0301500, NSFC, under Grants Nos. 11434015, 61227902

Funding

Funding support for this study was received from the National Key R & D Program of China under Grant No. 2016YFA0301500, NSFC, under grants Nos. 11434015 and 61227902 and from the Chennai Institute of Technology, Chennai, India, via funding number CIT/CNS/2023/RP-016.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon

    Nathan Tchepemen

  2. Centre for Computational Modeling, Chennai Institute of Technology, Chennai, Tamil Nadu, 600 069, India

    Sudharsan Balasubramanian

  3. Department of Physics, Indian Institute of Technology, Kandi, Telangana, 502285, India

    Nithyanandan Kanagaraj

  4. School of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Emmanuel Kengne

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  1. Nathan Tchepemen
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  3. Nithyanandan Kanagaraj
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NT and EK were involved in conceptualization, methodology, software, writing—original draft, investigation, data curation, visualization, and writing—reviewing and editing. SB and NK were responsible for methodology, software, investigation, and writing—reviewing and editing.

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Correspondence to Emmanuel Kengne.

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Nathan Tchepemen dedicates this work to his lovely daughter Leticia Njeukoue and spouse Micaise Kenfack.

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Tchepemen, N., Balasubramanian, S., Kanagaraj, N. et al. Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities. Nonlinear Dyn 111, 20311–20329 (2023). https://doi.org/10.1007/s11071-023-08951-4

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