Chaotic Solitons in a Plasma Driven by an rf Field

Nozaki, Kazuhiro; Bekki, Naoaki

doi:10.1143/jpsj.54.2363

Cited by 49 publications

(48 citation statements)

References 7 publications

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“…It also indicates that the soliton interacts most intensively with radiation waves near the lower boundary of their spectrum (where k = 0). This seems to be in agreement with earlier suggestions -made for a closely related externally driven NLS -that keeping just the k = 0 mode is sufficient to capture the basic features of the partial differential equation [33,34,35]. Accordingly, we focus our subsequent efforts on the verification of this hypothesis.…”

Section: Introductionsupporting

confidence: 89%

“…On the contrary, our approach allows to explore, systematically, each part of the phase space and identify the nonlinear modes responsible for each particular dynamical effect. Next, our reduction technique is different from the approach of an influential paper [33] which is also partially based on the Inverse Scattering. Besides the fact that the analysis of Ref.…”

Section: Discussionmentioning

confidence: 99%

“…Besides the fact that the analysis of Ref. [33] relies on the smallness of the perturbation, it only uses the Inverse Scattering transform to obtain the functional form of the radiation wave whereas its interaction with the soliton is introduced variationally. The damping term for the radiation was not part of the variational algorithm and had to be added in an ad-hoc way.…”

Section: Discussionmentioning

confidence: 99%

“…Unlike Ref. [33], our finite-dimensional reduction is uniquely defined by the choice of the ingredients of the localised attractor and does not require introduction of any phenomenological terms or fitting parameters. This uniqueness is reflected by the fact that (the linearisation of) our reduced system retains the self-similarity invariance of the (linearised) PDE.…”

Section: Discussionmentioning

confidence: 99%

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Soliton–radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

Shchesnovich

Barashenkov

2002

Physica D: Nonlinear Phenomena

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We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to previously utilised Inverse Scattering-based perturbation techniques, our approach is valid for arbitrarily large driving strengths and damping coefficients. We show that, contrary to suggestions made in literature, the complexity observed in the soliton's dynamics cannot be accounted for just by its coupling to the long-wavelength radiation.

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Section: Introductionsupporting

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Soliton–radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

Shchesnovich

Barashenkov

2002

Physica D: Nonlinear Phenomena

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“…Among others, LL equation has a number of dynamic solutions including the so called Kuznetsov-Ma (KM) solitons [215][216][217] and Akhmediev breathers (AB) [218,219]. These solutions correspond to time dependent envelope pulses formed on a finite background plain wave and belong to a general class of time dependent dissipative solitons that exist in various physical systems [220,221].…”

Section: Breathersmentioning

confidence: 99%

On Frequency Combs in Monolithic Resonators

2016

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Optical frequency combs have become indispensable in astronomical measurements, biological fingerprinting, optical metrology, and radio frequency photonic signal generation. Recently demonstrated microring resonator-based Kerr frequency combs point the way towards chip scale optical frequency comb generator retaining major properties of the lab scale devices. This technique is promising for integrated miniature radiofrequency and microwave sources, atomic clocks, optical references and femtosecond pulse generators. Here we present Kerr frequency comb development in a historical perspective emphasizing its similarities and differences with other physical phenomena. We elucidate fundamental principles and describe practical implementations of Kerr comb oscillators, highlighting associated solved and unsolved problems.

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Temporal Cavity Solitons in Kerr Media

Coen

Erkintalo

2015

Nonlinear Optical Cavity Dynamics

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Chaotic Solitons in a Plasma Driven by an rf Field

Cited by 49 publications

References 7 publications

Soliton–radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

Soliton–radiation coupling in the parametrically driven, damped nonlinear Schrödinger equation

On Frequency Combs in Monolithic Resonators

Temporal Cavity Solitons in Kerr Media

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