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Bright-Dark and Multi Solitons Solutions of (3 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability+

Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China
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Entropy 2020, 22(2), 202; https://doi.org/10.3390/e22020202
Received: 18 January 2020 / Revised: 30 January 2020 / Accepted: 2 February 2020 / Published: 10 February 2020
In this paper, bright-dark, multi solitons, and other solutions of a (3 + 1)-dimensional cubic-quintic complex Ginzburg–Landau (CQCGL) dynamical equation are constructed via employing three proposed mathematical techniques. The propagation of ultrashort optical solitons in optical fiber is modeled by this equation. The complex Ginzburg–Landau equation with broken phase symmetry has strict positive space–time entropy for an open set of parameter values. The exact wave results in the forms of dark-bright solitons, breather-type solitons, multi solitons interaction, kink and anti-kink waves, solitary waves, periodic and trigonometric function solutions are achieved. These exact solutions have key applications in engineering and applied physics. The wave solutions that are constructed from existing techniques and novel structures of solitons can be obtained by giving the special values to parameters involved in these methods. The stability of this model is examined by employing the modulation instability analysis which confirms that the model is stable. The movements of some results are depicted graphically, which are constructive to researchers for understanding the complex phenomena of this model.
Keywords: modified extended simple equation and exp(-ϕ(ξ))-expansion methods; proposed F- Expansion method; cubic-quintic complex Ginzburg–Landau equation; multi solitons; periodic solutions; solitary wave solutions modified extended simple equation and exp(-ϕ(ξ))-expansion methods; proposed F- Expansion method; cubic-quintic complex Ginzburg–Landau equation; multi solitons; periodic solutions; solitary wave solutions
MDPI and ACS Style

Yue, C.; Lu, D.; Arshad, M.; Nasreen, N.; Qian, X. Bright-Dark and Multi Solitons Solutions of (3 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability+. Entropy 2020, 22, 202.

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