×

zbMATH — the first resource for mathematics

Mutual transitions between stationary and moving dissipative solitons. (English) Zbl 1451.78018
Summary: Application of stable localized dissipative solitons as basic carriers of information promises the significant progress in the development of new optical communication networks. The success development of such systems requires getting the full control over soliton waveforms. In this paper we use the fundamental model of dissipative solitons in the form of the complex Ginzburg-Landau equation with a potential term to demonstrate controllable transitions between different types of coexisted waveforms of stationary and moving dissipative solitons. Namely, we consider mutual transitions between so-called plain (fundamental soliton), composite, and moving pulses. We found necessary features of transverse spatial distributions of locally applied (along the propagation distance) attractive potentials to perform those waveform transitions. We revealed that a one-peaked symmetric potential transits the input pulses to the plain pulse, while a two-peaked symmetric (asymmetric) potential performs the transitions of the input pulses to the composite (moving) pulse.
MSC:
78A40 Waves and radiation in optics and electromagnetic theory
35C08 Soliton solutions
35Q60 PDEs in connection with optics and electromagnetic theory
35Q56 Ginzburg-Landau equations
Software:
GPELab; GSGPEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Dissipative Solitons (2005), Springer: Springer Berlin · Zbl 1061.35003
[2] Dissipative Solitons: From Optics to Biology and Medicine (2008), Springer: Springer Berlin · Zbl 1147.35049
[3] Purwins, H.-G.; Bödeker, H.; Amiranashvili, Sh., Dissipative solitons, Adv. Phys., 59, 485-701 (2010)
[4] Liehr, A., Dissipative Solitons in Reaction Diffusion Systems (2013), Springer: Springer Berlin · Zbl 1270.92001
[5] Skarka, V.; Aleksić, N. B.; Lekić, M.; Aleksić, B. N.; Malomed, B. A.; Mihalache, D.; Leblond, H., Formation of complex two-dimensional dissipative solitons via spontaneous symmetry breaking, Phys. Rev. A, 90, Article 023845 pp. (2014)
[6] Cross, M. C.; Hohenberg, P. C., Pattern formation outside of equilibrium, Rev. Modern Phys., 65, 851-1112 (1993) · Zbl 1371.37001
[7] Aranson, I. S.; Kramer, L., The world of the complex Ginzburg-Landau equation, Rev. Modern Phys., 74, 99-143 (2002) · Zbl 1205.35299
[8] García-Morales, V.; Krischer, K., The complex Ginzburg-Landau equation: an introduction, Contemp. Phys., 53, 79-95 (2012)
[9] Boardman, A.; Velasco, L.; Egan, P., Dissipative magneto-optic solitons, (Akhmediev, N.; Ankiewicz, A., Dissipative Solitons (2005), Springer: Springer Berlin), 19-37 · Zbl 1080.35548
[10] Boardman, A. D.; Velasco, L., Gyroelectric cubic-quintic dissipative solitons, IEEE J. Sel. Top. Quantum Electron., 12, 388-397 (2006)
[11] Grelu, P.; Akhmediev, N., Dissipative solitons for mode-locked lasers, Nat. Phot., 6, 84-92 (2012)
[12] Akhmediev, N.; Ankiewicz, A., Dissipative solitons in the complex Ginzburg-Landau and Swift-Hohenberg equations, (Akhmediev, N.; Ankiewicz, A., Dissipative Solitons (2005), Springer: Springer Berlin), 1-17 · Zbl 1080.35133
[13] Malomed, B. A., Evolution of nonsoliton and “quasi-classical” wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations, Physica D, 29, 155-172 (1987) · Zbl 0635.35082
[14] Malomed, B. A.; Nepomnyashchy, A. A., Kinks and solitons in the generalized Ginzburg-Landau equation, Phys. Rev. A, 42, 6009-6014 (1990)
[15] Fauve, S.; Thual, O., Solitary waves generated by subcritical instabilities in dissipative systems, Phys. Rev. Lett., 64, 282-284 (1990)
[16] van Saarloos, W.; Hohenberg, P. C., Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations, Physica D, 56, 303-367 (1992) · Zbl 0763.35088
[17] Afanasjev, V. V.; Akhmediev, N.; Soto-Crespo, J. M., Three forms of localized solutions of the quintic complex Ginzburg-Landau equation, Phys. Rev. E, 53, 1931-1939 (1996)
[18] Renninger, W. H.; Chong, A.; Wise, F. W., Dissipative solitons in normal-dispersion fiber lasers, Phys. Rev. A, 77, Article 023814 pp. (2008)
[19] Deissler, R. J.; Brand, H. R., Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation, Phys. Rev. Lett., 72, 478-481 (1994)
[20] Soto-Crespo, J. M.; Akhmediev, N.; Ankiewicz, A., Pulsating, creeping, and erupting solitons in dissipative systems, Phys. Rev. Lett., 85, 2937-2940 (2000)
[21] Akhmediev, N.; Soto-Crespo, J. M.; Town, G., Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach, Phys. Rev. E, 63, Article 056602 pp. (2001)
[22] Soto-Crespo, J. M.; Akhmediev, N.; Chiang, K. S., Simultaneous existence of a multiplicity of stable and unstable solitons in dissipative systems, Phys. Lett. A, 291, 115-123 (2001) · Zbl 0980.35156
[23] Cundiff, S. T.; Soto-Crespo, J. M.; Akhmediev, N., Experimental evidence for soliton explosions, Phys. Rev. Lett., 88, Article 073903 pp. (2002)
[24] Descalzi, O.; Cartes, C.; Cisternas, J.; Brand, H. R., Exploding dissipative solitons: The analog of the Ruelle-Takens route for spatially localized solutions, Phys. Rev. E, 83, Article 056214 pp. (2011)
[25] Chang, W.; Soto-Crespo, J. M.; Vouzas, P.; Akhmediev, N., Extreme amplitude spikes in a laser model described by the complex Ginzburg-Landau equation, Opt. Lett., 40, 2949-2952 (2015)
[26] Chang, W.; Soto-Crespo, J. M.; Vouzas, P.; Akhmediev, N., Spiny solitons and noise-like pulses, J. Opt. Soc. Amer. B, 32, 1377-1383 (2015)
[27] Soto-Crespo, J. M.; Devine, N.; Akhmediev, N., Dissipative solitons with extreme spikes: Bifurcation diagrams in the anomalous dispersion regime, J. Opt. Soc. Amer. B, 34, 1542-1549 (2017)
[28] Akhmediev, N. N.; Ankiewicz, A.; Soto-Crespo, J. M., Multisoliton solutions of the complex Ginzburg-Landau equation, Phys. Rev. Lett., 79, 4047-4051 (1997) · Zbl 0947.35151
[29] Turaev, D.; Vladimirov, A. G.; Zelik, S., Chaotic bound state of localized structures in the complex Ginzburg-Landau equation, Phys. Rev. E, 75, Article 045601 pp. (2007)
[30] Descalzi, O.; Brand, H. R.; Cisternas, J., Hysteretic behavior of stable solutions at the onset of a weakly inverted instability, Physica A, 371, 41-45 (2006)
[31] Soto-Crespo, J. M.; Akhmediev, N., Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic Swift-Hohenberg equation, Phys. Rev. E, 66, Article 066610 pp. (2002)
[32] Achilleos, V.; Bishop, A. R.; Diamantidis, S.; Frantzeskakis, D. J.; Horikis, T. P.; Karachalios, N. I.; Kevrekidis, P. G., Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos, Phys. Rev. E, 94, Article 012210 pp. (2016)
[33] Sakaguchi, H.; Skryabin, D. V.; Malomed, B. A., Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion, Opt. Lett., 43, 2688-2691 (2018)
[34] Uzunov, I. M.; Georgiev, Z. D.; Arabadzhiev, T. N., Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects, Phys. Rev. E, 97, Article 052215 pp. (2018)
[35] Sugavanam, S.; Tarasov, N.; Wabnitz, S.; Churkin, D. V., Ginzburg-Landau turbulence in quasi-cw Raman fiber lasers, Laser Photonics Rev., 9, L35-L39 (2015)
[36] Malomed, B. A., Solitary pulses in linearly coupled Ginzburg-Landau equations, Chaos, 17, Article 037117 pp. (2007) · Zbl 1163.37351
[37] Descalzi, O.; Brand, H. R., Interaction of exploding dissipative solitons, Eur. Phys. J. B, 88, 219 (2015)
[38] Descalzi, O.; Brand, H. R., Collisions of non-explosive dissipative solitons can induce explosions, Chaos, 28, Article 075508 pp. (2018)
[39] Malomed, B. A., Soliton Management in Periodic Systems (2006), Springer: Springer Berlin · Zbl 1214.35056
[40] Ostrovskaya, E. A.; Abdullaev, J.; Desyatnikov, A. S.; Fraser, M. D.; Kivshar, Y. S., Dissipative solitons and vortices in polariton Bose-Einstein condensates, Phys. Rev. A, 86, Article 013636 pp. (2012)
[41] Smirnov, L. A.; Smirnova, D. A.; Ostrovskaya, E. A.; Kivshar, Y. S., Dynamics and stability of dark solitons in exciton-polariton condensates, Phys. Rev. B, 89, Article 235310 pp. (2014)
[42] Battogtokh, D.; Mikhailov, A., Controlling turbulence in the complex Ginzburg-Landau equation, Physica D, 90, 84-95 (1996) · Zbl 0884.35145
[43] Xiao, J.; Hu, G.; Yang, J.; Gao, J., Controlling turbulence in the complex Ginzburg-Landau equation, Phys. Rev. Lett., 81, 5552-5555 (1998) · Zbl 1223.81074
[44] Caliari, M.; Rainer, S., Gsgpes: A matlab code for computing the ground state of systems of gross – pitaevskii equations, Comput. Phys. Comm., 184, 812-823 (2013) · Zbl 1302.35004
[45] Antoine, X.; Bao, W.; Besse, C., Computational methods for the dynamics of the nonlinear schrödinger/gross – pitaevskii equations, Comput. Phys. Comm., 184, 2621-2633 (2013) · Zbl 1344.35130
[46] Antoine, X.; Duboscq, R., Gpelab a matlab toolbox to solve gross – pitaevskii equations i: Computation of stationary solutions, Comput. Phys. Comm., 185, 2969-2991 (2014) · Zbl 1348.35003
[47] Antoine, X.; Duboscq, R., Gpelab, a matlab toolbox to solve gross – pitaevskii equations ii: Dynamics and stochastic simulations, Comput. Phys. Comm., 193, 95-117 (2015) · Zbl 1344.82004
[48] Fratalocchi, A.; Assanto, G., Governing soliton splitting in one-dimensional lattices, Phys. Rev. E, 73, Article 046603 pp. (2006)
[49] Holmer, J.; Marzuola, J.; Zworski, M., Soliton splitting by external delta potentials, J. Nonlinear Sci., 17, 349-367 (2007) · Zbl 1128.35384
[50] Yang, R.; Wu, X., Spatial soliton tunneling, compression and splitting, Opt. Express, 16, 17759-17767 (2008)
[51] He, Y.-J.; Malomed, B. A.; Ye, F.; Hu, B., Dynamics of dissipative spatial solitons over a sharp potential, J. Opt. Soc. Amer. B, 27, 1139-1142 (2010)
[52] Yin, C.; Mihalache, D.; He, Y., Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential, J. Opt. Soc. Amer. B, 28, 342-346 (2011)
[53] Liu, B.; He, X.-D.; Li, S.-J., Continuous emission of fundamental solitons from vortices in dissipative media by a radial-azimuthal potential, Opt. Express, 21, 5561-5566 (2013)
[54] Boardman, A. D.; Xie, K., Magnetic control of optical spatial solitons, Phys. Rev. Lett., 75, 4591-4594 (1995)
[55] Boardman, A. D.; Xie, K., Magneto-optic spatial solitons, J. Opt. Soc. Amer. B, 14, 3102-3109 (1997)
[56] Boardman, A. D.; Xie, M., Spatial solitons in discontinuous magneto-optic waveguides, J. Opt. B: Quantum Semiclass. Opt, 3, S244 (2001)
[57] Boardman, A. D.; Xie, M.; Xie, K., Surface magneto-optic solitons, J. Phys. D: Appl. Phys., 36, 2211 (2003)
[58] Boardman, A. D.; Xie, M.; Xie, K., Spatial bright-dark solitons in transversely magnetized coupled waveguides, J. Opt. Soc. Amer. B, 22, 220-227 (2005)
[60] Kochetov, B. A.; Vasylieva, I.; Kochetova, L. A.; Sun, H.-B.; Tuz, V. R., Control of dissipative solitons in a magneto-optic planar waveguide, Opt. Lett., 42, 531-534 (2017)
[61] Kochetov, B. A.; Tuz, V. R., Cascade replication of dissipative solitons, Phys. Rev. E, 96, Article 012206 pp. (2017)
[62] Kochetov, B. A.; Tuz, V. R., Replication of dissipative vortices modeled by the complex Ginzburg-Landau equation, Phys. Rev. E, 98, Article 062214 pp. (2018)
[63] Kochetov, B. A.; Tuz, V. R., Induced waveform transitions of dissipative solitons, Chaos, 28, Article 013130 pp. (2018) · Zbl 1390.35348
[64] Liu, B.; He, Y.-J.; Malomed, B. A.; Wang, X.-S.; Kevrekidis, P. G.; Wang, T.-B.; Leng, F.-C.; Qiu, Z.-R.; Wang, H.-Z., Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials, Opt. Lett., 35, 1974-1976 (2010)
[65] Liu, B.; He, X.-D., Continuous generation of “light bullets” in dissipative media by an annularly periodic potential, Opt. Express, 19, 20009-20014 (2011)
[66] Cox, S.; Matthews, P., Exponential time differencing for stiff systems, J. Comput. Phys., 176, 430-455 (2002) · Zbl 1005.65069
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.