KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
1492–1512
Yayın Tarihi
2023-11-03
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:We mainly consider the case of $\alpha\neq 2\beta$ which is not discussed in previous work.
💡
Sonuç & Katkı:Some new traveling wave solutions of this equation are obtained including the compactons and the bounded solutions corresponding to some bounded manifolds.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. E. Aksoy, M. Kaplan and A. Bekir, Exponential rational function method for space-time fractional differential equations, Waves Random Complex Media 26 (2), 142-151, 2016
  2. S. Arshed, Soliton solutions of fractional complex Ginzburg-Landau equation with Kerr law and non-Kerr law media, Optik 160, 322-332, 2018
  3. A. Bekir and Ö. Güner, The (G'/G)-expansion method using modified Riemann-Liouville derivative for some space-time fractional differential equations. Ain Shams Eng. J. 5 (3), 959-965, 2014
  4. M. Caputo and F. Mainardi, Linear models of dissipation in anelastic solids, Riv. Nuovo Cimento (Ser. II) 1 (2), 161-198, 1971
  5. M. Caputo and F. Mainardi, A new dissipation model based on memory mechanism, Pure Appl. Geophys. 91, 134-147, 1971
  6. M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geophys. J. R. Astr. Soc. 13 (5), 529-539, 1967
  7. M.M. Djrbashian and A.B. Nersesian, Fractional derivative and the Cauchy problem for differential equations of fractional order, Izv. Acad. Nauk. Armjanskoi SSR 3 (1), 3-29, 1968
  8. C. Huang and Z. Li, New exact solutions of the fractional complex Ginzburg-Landau equation, Math. Probl. Eng. 2021 (2021)
  9. A. Hussain, A. Jhangeer et al., Optical solitons of fractional complex Ginzburg-Landau equation with conformable, beta, and M-truncated derivatives: a comparative study, Adv. Differ. Equ. 2020 (1), 1-19, 2020
  10. X. Jiang and H. Qi, Thermal wave model of bioheat transfer with modified Riemann-Liouville fractional derivative, J. Phys. A. Math. Theor. 45 (48), 485101, 2012
  11. G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. Math. Appl. 51, 1367-1376, 2006
  12. G. Jumarie, Stochastic differential equations with fractional Brownian motion input, J. Comput. System Sci. 3 (6), 1113-1132, 1993
  13. G. Jumarie, Fourier’s transform of fractional order via Mittag-Leffler function and modified Riemann-Liouville derivative, J. Appl. Math. Inform. 26, 1101-1121, 2008
  14. G. Jumarie, Laplace’s transform of fractional order via the Mittag-Leffler function and modified Riemann-Liouville derivative, Appl. Math. Lett. 22 (11), 1659-1664, 2009
  15. E. Kengne, A. Lakhssassi et al., Exact solutions for generalized variable-coefficients Ginzburg-Landau equation: Application to Bose-Einstein condensates with multi-body interatomic interactions, J. Math. Phys. 53 (12), 123703, 2012