Stability of Dissipative Optical Solitons in the 2D Complex Swift-Hohenberg Equation

P. Yoboue¹, A. Diby², O. Asseu^{1, 3,} and A. Kamagate¹

¹Ecole Supérieure Africaine des Technologies d’Information et de Communication (ESATIC), Abidjan, Côte d’Ivoire

²Université Félix Houphouët Boigny, Abidjan, Côte d’Ivoire

³Institut National Polytechnique Félix Houphouët Boigny (INP-HB), Yamoussoukro, Côte d’Ivoire

Cite this paper:
P. Yoboue, A. Diby, O. Asseu and A. Kamagate. Stability of Dissipative Optical Solitons in the 2D Complex Swift-Hohenberg Equation. International Journal of Physics. 2016; 4(4):78-84. doi: 10.12691/ijp-4-4-2

Abstract

This article deals with stationary localized solutions of the (2D) two-dimensional complex Swift-Hohenberg equation (CSHE). Our approach is based on the semi-analytical method of collective coordinate approach. According to the parameters of the equation and a suitable choice of ansatz, the stationary dissipative solitons of the 2D CSHE equation are mapped. This approach allows to describe the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Finally, the major impact of spectral filtering terms on the dynamic of the solitons is demonstrated.

Keywords:
dissipative soliton spatio-temporal collective coordinate approach Ginzburg-Landau equation complex Swift-Hohenberg equation spectral filtering

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References:

[1]	Y. Silberberg, Collapse of optical pulses, Optics Letters 15 (1990), 1282-1284.
[2]	N. N. Rosanov, Spatial hysteresis and optical patterns, Springer Berlin, 2002.
[3]	N. Akhmediev and A. Ankiewicz, Solitons Around Us: Integrable, Hamiltonian and Dissipative Systems, Lecture Notes in Physics, Springer, Heidelberg, 2003.
[4]	N. Akhmediev and A. Ankiewicz, Dissipative solitons. Ed. Springer, Heidelberg, 2005.
[5]	N. Akhmediev and A. Ankiewicz, Dissipative solitons: from optics to biology and medicine, Springer, Heidelberg, 2008.
[6]	Q. Zhou, Y. Zhong, M. Mirzazadeh, A.H. Bhrawy, E. Zerrad and A. Biswas, Thirring combo solitions with cubic nonlinearity and spatio-temporal dispersion, Waves in Random and Complex Media. Vol. 26 (2016), Issue 2, 204-210.
[7]	Q. Zhou, M. Mirzazadeh, E. Zerrad, A. Biswas and M. Belic, Bright, dark and singular solitons in optical fibers with spatio-temporal dispersion and spatially-dependent coefficients, Journal of Modern Optics. Vol. 63 (2016), Number 10, 950-954.
[8]	M. Mirzazadeh, M. Eslami, M. Savescu, A. H. Bhrawy, A. A. Alshaery, E. M. Hilal and A. Biswas, Optical solitons in dwdmsystem with spatio-temporal dispersion, Journal of Nonlinear Optical Physics and Materials. Vol. 24 (2015), Issue 1, 1550006.
[9]	J.M. Soto Crespo, Ph. Grelu and N. Akhmediev, Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions, Optics Express 14 (2006), 4013-4025.
[10]	J.M. Soto Crespo, N. Akhmediev and Ph. Grelu, Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes, CHAOS 17 (2007), 037112.
[11]	A. H. Arnous, M. Mirzazadeh, S. Moshokoa, S. Medhekar, Q. Zhou, M. F. Mahmood, A. Biswas and M. Belic, Solitons in optical metamaterials with trial solution approach and backlund transform of riccati equation, Journal and Computational and Theoretical Nanoscience. Vol. 12 (2015), Number 12, 5940-5948.
[12]	V. Skarla and N. Aleksic, Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations, Phys. Rev. Lett. 96 (2006), 013903.
[13]	A. Kamagaté, Ph. Grelu, P. Tchofo-Dinda, J.M. Soto-Crespo, N. Akhmediev, Stationary and pulsating dissipative light bullets from a collective variable approach. Phys. Rev. E, 2009, 79, 026609.
[14]	M. Mirzazadeh, M. F. Mahmood, F. B. Majid, A. Biswas and M. Belic, Optical solitons in birefringent fibers with riccati equation method, Optoelectronics and Advanced Materials - Rapid Communications. Vol. 9 (2015), Numbers7-8, 1032-1036.
[15]	P. Tchofo-Dinda, A.B. Moubissi, K. Nakkeeran, Collective variable theory for optical solitons in fibers. Phys Rev. E, 64 (2001), 016608.
[16]	G. Nicolis and I. Prigogine, Self-organization in nonequilibrium systems - From dissipative structures to order through fluctuations, John Wiley \& sons, New York,1977.
[17]	W.V. Saarlos and P.C. Hhenberg, Fronts, pulse, sources and sinks in generalized Ginzburg-Landau. Physica D, 56 (1992), 303-367.
[18]	N. Bekki and K. Nozaki, Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation, Phys. Lett., 110 (1985), 133-135.
[19]	N. Akhmediev and V.V. Afanasjev, Novel arbitrary-amplitude soliton solutions of cubic-quintic complex Ginzburg-Landau equation, Phys. Rev. Lett., 75 (1995), 2320-2323.
[20]	Y. Kuramoto, Chemical Oscillations, Waves and Turbulence Dissipative Solitons, Springer-Verglag, Berlin, 1984.
[21]	C. Normand, Y. Pomeau, M.G. Velarde, Convective instability: A physicist’s approach, Rev. Mod. Phys., 49 (1977), 581-624.
[22]	N. Akhmediev and A. Ankiewicz, Solitons of the Complex Ginzburg-Landau equation, Springer, Berlin, 2001.
[23]	P.A. Belanger, Coupled-cavity mode-locking: a nonlinear model, J. Opt. Soc. Am. B, 8 (1991), 2077-2082.
[24]	J.D. Moores, On the Ginzburg-Landau laser mode-locking model with fifth-oder saturable absorber term, Opt. commun., 96 (1993), 65-70.
[25]	L.F. Mollenauer, J.P. Gordon and S.G. Evangelides, The sliding-frequency guiding: an improved from soliton jitter control, Opt. Lett., 1992, vol.17 (1992), 1575-1577.
[26]	W.J. Firth and A.J. Scroggie, Optical bullet holes: Robust controllable localized states of a nonlinear cavity, Phys. Rev. Lett., 76 (1996), 1623-1626.
[27]	P.S. Jian, W.E. Torruellas, M. Haelterman, U. Peschel and F. Lederer, Solitons of singly resonant optical parametric oscillators, Opt. Lett, 24 (1994), 400-402.
[28]	M. Mirzazadeh, A. H. Arnous, M. F. Mahmood, E. Zerrad and A. Biswas, Solitons solutions to resonant nonlinear Schrodinger’s equation with time dependent coefficients by trial solution approach, Nonlinear Dynamics. Vol. 81 (2015), Issue 1-2. 277-282.