Quiescent optical solitons with complex Ginzburg–Landau equation having a dozen forms of self–phase modulation [PDF]
Heliyon, 2023 The current study focuses on the recovery of quiescent optical solitons through the use of the complex Ginzburg–Landau equation when the chromatic dispersion is rendered to be nonlinear.
Ahmed H. Arnous +5 more
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Results in Physics, 2022 This paper secures exact solutions from perturbed complex Ginzburg–Landau equation that is taken into account with Kerr law and cubic–quintic–septic nonlinearity.
Ming-Yue Wang
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Analytical wave families and stability dynamics in a modified complex Ginzburg–Landau model via the modified extended direct algebraic method [PDF]
Scientific ReportsThis study investigates the Modified Complex Ginzburg–Landau Equation, a fundamental nonlinear partial differential equation that plays a central role in modeling complex wave dynamics, pattern formation, and dissipative phenomena in systems such as ...
Adel E. Rateb +4 more
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Solving generalized quintic complex Ginzburg–Landau equation by homotopy analysis method
Ain Shams Engineering Journal, 2018 In this paper, the generalized quintic complex Ginzburg–Landau equation is considered to be solved, by means of the homotopy analysis method (HAM). Two examples are solved to illustrate the efficiency of the proposed method.
Soheila Naghshband +1 more
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Finite-Time Blowup for a Complex Ginzburg--Landau Equation [PDF]
SIAM Journal on Mathematical Analysis, 2013 We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-iθ} u_t = Δu+ |u|^α u$ blow up in finite time, where α>0 and π ...
Flavio Dickstein +2 more
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Propagation of solitary waves for hydrodynamical nonlinear complex model in a fractional derivative setting [PDF]
Scientific ReportsThis study investigates soliton solutions and dynamic wave behaviors in the complex Ginzburg–Landau equation, a model that plays a central role in describing diverse physical phenomena such as superconductivity, nonlinear optical fibers, liquid crystals,
Muhammad Bilal +6 more
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The inviscid limit for the complex Ginzburg–Landau equation
Journal of Mathematical Analysis and Applications, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuji Machihara
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Existence of standing waves for the complex Ginzburg–Landau equation
Journal of Mathematical Analysis and Applications, 2015 We prove the existence of non-trivial standing wave solutions of the complex Ginzburg-Landau equation $ϕ_t - e^{iθ}(ρI- Δ) φ- e^{iγ} |ϕ|^αφ=0 $ in $\Rn$, where $(N-2)α<4$, $θ,γ\in (-π/2,π/2)$ and $ρ>0$. Analogous result is obtained in a ball $Ω\in\Rn$ for $ρ>-λ_1$, where $λ_1$ is the first eigenvalue of the Laplace operator with Dirichlet ...
Flavio Dickstein +2 more
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The world of the complex Ginzburg-Landau equation [PDF]
Reviews of Modern Physics, 2002 Submitted to Reviews of Modern Physics, reduced resolution ...
Aranson, Igor S., Kramer, Lorenz
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Multisoliton Solutions of the Complex Ginzburg-Landau Equation [PDF]
Physical Review Letters, 1997 We present novel stable solutions which are soliton pairs and trains of the ID complex Ginzburg-Landau equation (CGLE), and analyze them. We propose that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations.
Akhmediev, N. +2 more
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