Exact Solutions and Stability Analysis of Pulse-Front Pairs in Coupled Complex Ginzburg–Landau Equations
DOI:
https://doi.org/10.24297/jam.v24i.9764Keywords:
explicit exact solutions, Painlevé analysis, modified Hirota bilinear method, solitary pulses and fronts, coupled complex Ginzburg–Landau equationsAbstract
This work introduces new exact solutions demonstrating how localized pulses and fronts can coexist in coupled complex
Ginzburg–Landau systems. Using a novel analytical method, we establish conditions for the stability and phase-locking
of these structures, revealing relationships between amplitude, wave-number, and dispersion effects. In practical optical
setups like dual-core fibers, these solutions can produce stable wave patterns that transfer energy efficiently. Our
approach addresses existing difficulties in analyzing complex dissipative systems and enhances understanding of their
wave interactions.
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References
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Mod. Phys. 74 (2002),
–143. https://doi.org/10.1103/RevModPhys.74.99
F. T. Arecchi, S. Boccaletti, and P. L. Ramazza, Pattern formation and competition in nonlinear optics,
Phys. Rep. 318 (1999), 1–83. https://doi.org/10.1016/S0370-1573(99)00007-1
J. Atai and B. A. Malomed, Bound states of solitary pulses in coupled Ginzburg–Landau equations,
Phys. Lett. A 244 (1998), 551–556. https://doi.org/10.1016/S0375-9601(98)00308-9
C. Crawford and H. Riecke, Tunable front interaction in periodically forced waves, Phys. Rev. E 65 (2002), 066307.
https://doi.org/10.1103/PhysRevE.65.066307
E. O. Doro and C. K. Aidun, Interfacial waves and the dynamics of backflow in falling liquid films, J. Fluid Mech. 726
(2013), 261–284. https://doi.org/10.1017/jfm.2013.172
H. Herrero and H. Riecke, Bound pairs of fronts in a real Ginzburg–Landau equation coupled to a mean field,
Physica D 85 (1995), 79–92. https://doi.org/10.1016/0167-2789(95)00068-F
W. Hong, On generation of coherent structures induced by modulational instability in linearly coupled cubic–quintic
Ginzburg–Landau equations, Opt. Commun. 281 (2008), 6112–6119.
https://doi.org/10.1016/j.optcom.2008.10.034
M. Ipsen, L. Kramer, and P. G. Sorensen, Amplitude equations for description of chemical reaction-diffusion
systems, Phys. Rep. 337 (2000), 193–235. https://doi.org/10.1016/S0370-1573(00)00062-4
C. K. Lam, K. W. Chow, and T. L. Yee, Phase Locked ‘Localized Pulse / Moving Front’ Pair in Coupled Complex
Ginzburg–Landau Equations. [Unpublished manuscript]
B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, Spatiotemporal optical solitons, J. Opt. B: Quantum Semi-
class. Opt. 7 (2005), R53–R72. https://doi.org/10.1088/1464-4266/7/5/R02
K. Nozaki and N. Bekki, Exact solutions of the generalized Ginzburg–Landau equation, J. Phys. Soc. Jpn. 53
(1984), 1581–1582. https://doi.org/10.1143/JPSJ.53.1581
H. Riecke and L. Kramer, The stability of standing waves with small group velocity, Physica D 137 (2000),
–142. https://doi.org/10.1016/S0167-2789(99)00123-2
D. L. M. Souza, F. D. S. Borges, and E. C. Gabrick, Spiral wave dynamics in a neuronal network model,
J. Phys. Complexity 5 (2024), 025010. https://doi.org/10.1088/2632-072X/ad42f6
K. Watanabe, R. Niigaki, T. Inoue, H. Thienpont, and N. Vermeulen, Highly Sensitive Dispersion Characteri-
zation of mm-Length Silicon Nitride Waveguides and Their Couplers Around the Zero-Dispersion Wavelength,
Adv. Opt. Mater. 13 (2024), 2402418. https://doi.org/10.1002/adom.202402418
T. L. Yee and K. W. Chow, A “Localized pulse-moving front" pair in a system of coupled complex Ginzburg–Landau
equations, J. Phys. Soc. Jpn. 79 (2010), 124003. https://doi.org/10.1143/JPSJ.79.124003
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