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Journals / Hacettepe Journal of Mathematics and Statistics / 2023 / Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications

Wave solutions of the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity

Niping CAİ
Yuqian ZHOU
Qian LİU
Pages
1492–1512
Publication Date
2023-11-03
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some new traveling wave solutions of this equation are obtained including the compactons and the bounded solutions corresponding to some bounded manifolds.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the bifurcation theory of dynamical system is applied to investigate the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity.
📊
Key Findings & Data:We mainly consider the case of $\alpha\neq 2\beta$ which is not discussed in previous work.
💡
Conclusion & Impact:Some new traveling wave solutions of this equation are obtained including the compactons and the bounded solutions corresponding to some bounded manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:bifurcation · dynamical system · fractional equation

Abstract

In this paper, the bifurcation theory of dynamical system is applied to investigate the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity. We mainly consider the case of $\alpha\neq 2\beta$ which is not discussed in previous work. By overcoming some difficulties aroused by the singular traveling wave system, such as bifurcation analysis of nonanalytic vector field, tracking orbits near the full degenerate equilibrium and calculation of complicated elliptic integrals, we give a total of 20 explicit exact traveling wave solutions of the time-space fractional complex Ginzburg-Landau equation and classify them into 11 categories. Some new traveling wave solutions of this equation are obtained including the compactons and the bounded solutions corresponding to some bounded manifolds.

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Cite This Article

CAİ, N., ZHOU, Y., LİU, Q. (2023). Wave solutions of the time-space fractional complex Ginzburg-Landau equation with Kerr law nonlinearity. Hacettepe Journal of Mathematics and Statistics, Cilt: 52 Sayı: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1492–1512. https://ajindex.com/articles/971782

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