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On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods

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Abstract

This paper analyzes the coupled nonlinear (2+1)-dimensional complex modified Korteweg-de-Vries (cmKdV) equation, which appears in the fields of applied magnetism and nanophysics. By taking advantage of two mathematical integration approaches, namely, the modified generalized exponential rational function method and the extended \(\tanh \) function method, a variety of exact optical soliton solutions are obtained for the governing cmKdV equation. These acquired soliton solutions are determined in terms of hyperbolic, exponential, and trigonometric function types. By choosing suitable values of parameters, some 3D, 2D, and contour plots are portrayed with the aid of symbolic computation in Mathematica to visualize the underlying dynamics of the generated solutions. These solutions include doubly soliton, multi-soliton, singular periodic soliton, anti-bell-shaped soliton, and hyperbolic structures. Moreover, the modulation instability of the governing equation is also investigated by using the linear stability analysis. The results presented in this paper are novel and are reported for the first time in the literature. Again, modulation instability analysis was carried out on the governing model for the first time. Thus, the results obtained demonstrate that the two new mathematical schemes are quite concise and effective and can be useful in understanding the dynamical behaviors of many other nonlinear physical models appearing in nonlinear optics, nanophysics, and so many other areas of nonlinear sciences.

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Acknowledgements

The authors would like to thank the Editor and the referees for their valuable, supportive, and helpful comments. Sachin Kumar, the author, would also like to thank the Science and Engineering Research Board SERB-DST, India for financial support provided through the MATRICS Scheme (MTR/2020/000531).

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  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Setu Rani, Sachin Kumar & Nikita Mann

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  1. Setu Rani
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Rani, S., Kumar, S. & Mann, N. On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods. Opt Quant Electron 55, 731 (2023). https://doi.org/10.1007/s11082-023-04946-y

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