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Multiple solitons solutions, lump solutions and rogue wave solutions of the complex cubic Ginzburg–Landau equation with the Hirota bilinear method

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Abstract

In this paper, we obtain the exact solutions of the (1+1) dimensional complex cubic Ginzburg–Landau equation (CCGLE) by using the Hirota bilinear method, this equation is a universal model for the evolution of the envelope of slowly varying waves packets in nonlinear dissipative media. Different types of solutions including solitons, lump and rogue wave solutions are gotten by taking different transformations. Besides, the physical significance of these solutions of CCGLE can be understood better through drawing \(\text{3D, } \text{2D }\) and contour plots.

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The datasets generated during the current study are not publicly available due to individual privacy but are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Natural Science Foundation of Shanxi (No. 202103021224068).

Funding

Funding was provided by Natural Science Foundation of Shanxi (Grant number: 202103021224068).

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Liu Yang & Ben Gao

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  1. Liu Yang
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  2. Ben Gao
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Correspondence to Ben Gao.

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Yang, L., Gao, B. Multiple solitons solutions, lump solutions and rogue wave solutions of the complex cubic Ginzburg–Landau equation with the Hirota bilinear method. Indian J Phys (2024). https://doi.org/10.1007/s12648-024-03242-z

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