Resonant control of solitons

Batalov, S. V.; Shagalov, A. G.

doi:10.1016/j.physleta.2013.01.046

Cited by 9 publications

(7 citation statements)

References 21 publications

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“…The development of the control algorithm is carried out on the basis of the speed-gradient method [12], which was previously used for oscillation control problems, see, for example, [12,16]. The feedback methods for nonlinear waves were developed in [1,2,7,8,10,11], while feed-forward (non-feedback) controlling actions were considered in [4][5][6]9]. The main feature of our method is the simultaneous inclusion of the desired shape and velocity of the wave in the feedback.…”

Section: Choice Of Control Methodsmentioning

confidence: 99%

“…Also, the control of the shape of the plane wave in reaction-diffusion systems is established in [2]. Similarly, the excitation and stable propagation of an envelope wave solution [6,9] or multi-phase sine-Gordon solutions [5] may be considered. The desired control behaviour of a periodic wave in reaction-diffusion systems was studied in [3], while control of the wave maximum to avoid blow-up has been considered in [7,8].…”

Section: Goal Of Nonlinear Wave Controlmentioning

confidence: 99%

“…There are a variety of control methods of nonlinear waves such as the sensitivity of the wave solutions to the type of nonlinear equation, the initial and boundary conditions, the aim of the control, etc. Thus, nonlinear reaction-diffusion systems were studied in [1][2][3], nonlinear modulation equations were considered in [4][5][6][7][8] and the sine-Gordon equation solutions were subjected to control in [9][10][11]. The control algorithm may be obtained using conservation laws: in most of the previous papers on this subject control problems were studied using asymptotic procedures that restrict consideration by small variations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control methods for localization of nonlinear waves

Порубов

Andrievsky

2017

Phil. Trans. R. Soc. A.

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A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.

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Section: Choice Of Control Methodsmentioning

confidence: 99%

Section: Goal Of Nonlinear Wave Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Control methods for localization of nonlinear waves

Порубов

Andrievsky

2017

Phil. Trans. R. Soc. A.

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“…[7][8][9] and references therein). The study of AR was further extended to multi-dimensional processes such as excitations of continuously phase-locked plasma waves [10], particle transport in a weak external field with slowly changing frequency [11], autoresonant excitation of solitons [12], control of nanoparticles and electron beams [13,14], etc. In most of these studies, AR in the forced oscillator was considered as an effective tool for exciting high-energy oscillations in the entire system.…”

Section: Introductionmentioning

confidence: 99%

Control of autoresonance in mechanical and physical models

Kovaleva¹

2017

Phil. Trans. R. Soc. A.

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Autoresonant energy transfer has been considered as one of the most effective methods of excitation and control of high-energy oscillations for a broad range of physical and engineering systems. Nonlinear time-invariant feedback control provides effective self-tuning and self-adaptation mechanisms targeted at preserving resonance oscillations under variations of the system parameters but its implementation may become extremely complicated. A large class of systems can avoid nonlinear feedback, still producing the required state due to time-variant feed-forward frequency control. This type of control in oscillator arrays employs an intrinsic property of a nonlinear oscillator to vary both its amplitude and the frequency when the driving frequency changes. This paper presents a survey of recently published and new results studying possibilities and limitations of time-variant frequency control in nonlinear oscillator arrays.This article is part of the themed issue 'Horizons of cybernetical physics'.

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“…Recently, the chaotic behavior of solitons have been observed experimentally for spin waves propagating in magnetic films [19]. It is resulted in a new wave of interest for both theoretical and experimental studies of chaotic dynamics of solitons [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. …”

mentioning

confidence: 99%

Analysis of chaotic bright spin-wave soliton trains in magnetic films

Устинов

Кондрашов

Никитин

2015

J. Phys.: Conf. Ser.

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Abstract.We have experimentally studied a chaotic dynamics of bright spin-wave soliton trains. Thin yttrium iron garnet films having pinned surface spins were used for the experiments providing propagation of highly dispersive dipole-exchange spin waves. Chaotic soliton trains were excited in the frequency band around low-frequency part of dipole gap of spin wave spectrum. Analysis of fractal dimension, embedding dimension, and Lyapunov exponents was carried out based on measured time profiles of chaotic soliton sequences. We find that the fractal dimension and Lyapunov exponents are weak function of carrier frequency around dipole gap whereas embedding dimension is almost constant. IntroductionEnvelope solitons are formed in the nonlinear dispersive waveguiding media with pulsed excitation if the dispersion spreading of a nonlinear wave packet is compensated by the media nonlinearity. Solitons are also formed with a monochromatic wave excitation through development of the spontaneous modulation instability (SMI) [1,2].Among other media, high-quality magnetic films, such as single-crystal yttrium iron garnet (YIG) films, were proven to be excellent objects for experiments on nonlinear wave phenomena with microwave spin waves. We underline, that it was the YIG films where a formation of the stationary soliton trains from a monochromatic spin wave (SW) through development of the spontaneous modulation instability (SMI) has been discovered and studied [3][4][5].Theoretically, the soliton as a stationary solution of the nonlinear Schrodinger (NLS) equation happens to be stable. Experimentally, the soliton is also usually considered as a stable excitation which preserves its shape and speed during propagation. At the same time, using an optical modelocked laser, Bolton and Acton [6] have demonstrated in 2000 year a chaotic behavior of solitons which represented pulsations in amplitude of optical pulses circulating in the optical cavity. After that considerable amount of theoretical work was devoted to study of possible chaotic behavior of solitons in the different physical systems [7][8][9][10][11][12][13]. The concept of "dissipative solitons" [14,15] resolves the contradiction.At present, studies on chaotic wave excitations in waveguiding media and auto-oscillators are of great interest both for basic research and for their possible applications in advanced optical and microwave communication technology [16][17][18]. Recently, the chaotic behavior of solitons have been observed experimentally for spin waves propagating in magnetic films [19]. It is resulted in a new wave of interest for both theoretical and experimental studies of chaotic dynamics of solitons [20][21][22][23][24][25][26][27][28][29][30][31][32][33].

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Resonant control of solitons

Abstract: It is shown that the effect of "scattering on resonance" can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton.Crown

Cited by 9 publications

References 21 publications

Control methods for localization of nonlinear waves

Control methods for localization of nonlinear waves

Control of autoresonance in mechanical and physical models

Analysis of chaotic bright spin-wave soliton trains in magnetic films

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