Abstract
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.
Highlights
The nonlinear Schrödinger’s equations (NLSEs) are well-known models in nonlinear partial differential equations (PDEs) to govern the optical soliton propagation [1,2,3,4,5,6,7,8,9,10,11,12,13]
The authors in [17] proposed one more complex division for NLSE wherein the function of the wave is separated into phase angle and amplitude
The propagation of ultrashort optical solitons in optical fiber is modeled by this equation
Summary
The nonlinear Schrödinger’s equations (NLSEs) are well-known models in nonlinear partial differential equations (PDEs) to govern the optical soliton propagation [1,2,3,4,5,6,7,8,9,10,11,12,13]. Entropy 2020, 22, 202 branches of science and plays an important role in practical applications including fluid dynamics, nonlinear optics, mathematical biology, hydro dynamical stability problems, condensed matter physics, Bose–Einstein condensates, chemical reactions, super conductivity, and quantum field theories [19,20,21,22,23] It demonstrates prosperous dynamics and has turned into an example for alterations to the chaos of spatio-temporal. In physics and applied mathematics, the different forms of complex Ginzburg–Landau equations have attained great attention from researchers, as universal models where the most interesting solutions are dissipative solitons. The aim is to construct the novel analytical solutions in different forms such as dark-bright solitons, multi solitons, kink and anti-kink waves, solitary wave, and trigonometric function solutions of (3 + 1)-dimensional CQCGLE via the modified extended simple equation method (MESEM), exp(−φ(ξ ))-expansion method and proposed F-Expansion method.
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