Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Anderson, Justin Q.; Ryan, Rachel; Wu, Mingzhong; Carr, Lincoln D.

doi:10.1088/1367-2630/16/2/023025

Cited by 11 publications

(17 citation statements)

References 59 publications

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“…The absence of these additional frequency modes here, as well as the lower than unity Jacobi-elliptic parameter, indicate that this solitary wave breathing dynamic occurs at lower ring gains than those which support bright soliton wave trains and where higher order losses impact dynamics. This matches the numerical predictions for regimes which support solitary wave periodic breathing where cubic losses were the highest relative loss [42]. A total of three distinct bright single periodic breathers were observed experimentally at increasing ring gain.…”

Section: A Bright Solitary Wave Periodic Breathingsupporting

confidence: 85%

“…These results are distinct from the study of dissipative solitons in the above mentioned systems where focus has generally remained on exploring transient behaviors, periodic modulations and isolating extreme events [38][39][40][41]. The behaviors described here were previously predicted to be observable by a numerical parameter space search which identified four distinct long lifetime examples of dynamical pattern formation in bright solitary waves described by the CQCGL [42]. We emphasize that these numerical predictions involved an extraordinarily broad parameter space search which spanned a minimum of five orders of magnitude for four distinct parameters (S, L, C and Q in equation 2).…”

Section: Introductionmentioning

confidence: 65%

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Physical realization of complex dynamical pattern formation in magnetic active feedback rings

Anderson,

Janantha,

Alcala

et al. 2020

Preprint

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We report the clean experimental realization of cubic-quintic complex Ginzburg-Landau physics in a single driven, damped system. Four numerically predicted categories of complex dynamical behavior and pattern formation are identified for bright and dark solitary waves propagating around an active magnetic thin film-based feedback ring: (1) periodic breathing; (2) complex recurrence; (3) spontaneous spatial shifting; and (4) intermittency. These nontransient, long lifetime behaviors are observed in microwave spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide operating in a ring geometry where the net losses are directly compensated for via linear amplification on each round trip O(100 ns). The behaviors exhibit periods ranging from tens to thousands of round trip times O(µs) and are stable for 1000s of periods O(ms). We present 10 observations of these dynamical behaviors which span the experimentally accessible ranges of attractive cubic nonlinearity, dispersion, and external field strength that support the self-generation of backward volume spin waves in a four-wave-mixing dominant regime. Three-wave splitting is not explicitly forbidden and is treated as an additional source of nonlinear losses. These long lifetime behaviors of bright solitary waves span the categories of dynamical behavior previously numerically predicted to be observable and represent a complete experimental verification of the cubic-quintic complex Ginzburg-Landau equation as a model for the study of fundamental, complex nonlinear dynamics for driven, damped waves evolving in nonlinear, dispersive systems. These observed behaviors are persistent over long times and robust over wide parameter regimes, making them very promising for technological applications. The dynamical pattern formation of self-generated dark solitary waves in attractive nonlinearity, however, is entirely novel and is reported for both the periodic breather and complex recurrence behaviors. All behaviors are identified in the group velocity co-moving frame. For (1) periodic breathing, we find that four or fewer bright or dark solitary waves may exhibit breathing with stable periods ranging from tens to hundreds of round trip times. The location of the solitary waves within the ring are seen to shift predictably while maintaining both peak solitary wave amplitudes and widths. For (2) complex recurrence, we find the periodic recurrence of interactions of three or more bright or dark solitary wave peaks is observed with stable recurrence times varying from hundreds to tens of thousands of round trips. For (3) spontaneous spatial shifting, we find spontaneous relocation of otherwise stable underlying ring dynamics is characterized by the instantaneous shift in location, in the group velocity frame, of the solitary waves while maintaining all other characteristics of the behavior. The time between shifts is unpredictable. Finally, for (4) intermittency, the dynamical behavior observed within the feedback ring shifts between two or more...

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Section: A Bright Solitary Wave Periodic Breathingsupporting

confidence: 85%

Section: Introductionmentioning

confidence: 65%

Physical realization of complex dynamical pattern formation in magnetic active feedback rings

Anderson,

Janantha,

Alcala

et al. 2020

Preprint

Self Cite

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“…Fig. 2(b), results from a relatively short evolution distance as well as higher-order nonlinearity 34,35 and nonlinear damping 35,36,37 that are neglected in the simulations. In summary, this work demonstrates self-cavitating envelope DSWs for spin waves.…”

Section: Figures 3 and 4 Present Data Revealing That Dsw Formation Ismentioning

confidence: 99%

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

et al. 2017

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The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin-wave step pulse in a low-loss magnetic Y 3 Fe 5 O 12 thin film strip, in which the spin-wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin-wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW selfcavitation, indicated by a point of zero power and a concomitant 180 phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

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“…ensures that the temporal correlations do not produce spurious attractor dimensions. We also check each parameter against perturbations in order to confirm that the attractor is invariant under smooth transformations [60].…”

Section: B Correlation Dimensionmentioning

confidence: 99%

Layered chaos in mean-field and quantum many-body dynamics

et al. 2019

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We investigate the dimension of the phase-space attractor of a quantum chaotic many-body ratchet in the meanfield limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes-Rabi oscillations, chaos, and self-trapping regimes-and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free noninteracting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of local density in each of the dynamical regimes has an attractor characterized by a higher fractal dimension, D R = 2.59 ± 0.01, D C = 3.93 ± 0.04, and D S = 3.05 ± 0.05, compared to the global measure of current, D R = 2.07 ± 0.02, D C = 2.96 ± 0.05, and D S = 2.30 ± 0.02. The deviation between local and global measurements of the attractor's dimension corresponds to an increase towards higher condensate depletion, which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number N, namely, as N β with β R = 0.51 ± 0.004 and β C = 0.18 ± 0.004 for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapping regimes but not in the chaotic regime, with revival times scaling linearly in particle number for Rabi dynamics. Based on the obtained results, we outline pathways for the identification and characterization of emergent phenomena in driven many-body systems. This includes the identification of many-body localization from the many-body measures of the system, the influence of entanglement on the rate of the convergence to the mean-field limit, and the establishment of a polynomial scaling of the Ehrenfest time at which the mean-field description fails to describe the dynamics of the system.

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Complex solitary wave dynamics, pattern formation and chaos in the gain–loss nonlinear Schrödinger equation

Cited by 11 publications

References 59 publications

Physical realization of complex dynamical pattern formation in magnetic active feedback rings

Physical realization of complex dynamical pattern formation in magnetic active feedback rings

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

Layered chaos in mean-field and quantum many-body dynamics

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