Ginzburg–Landau models of nonlinear electric transmission networks

Kengne, Emmanuel; Liu, Wu-Ming; English, Lars Q.; Malomed, Boris A.

doi:10.1016/j.physrep.2022.07.004

Cited by 52 publications

(14 citation statements)

References 326 publications

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“…A wide variety of processes and phenomena studied in the theory of phase transitions, laser and plasma physics, nonlinear optics, physics of electrical transmission lines and many other branches of natural sciences are modelled on the ground of the so-called derivative nonlinear Schrödinger equations which maid be thought of as generalizations of the standard nonlinear Schrödinger equation extended by appending different kinds of linear and nonlinear terms in order to capture the interplay between dispersive and nonlinear effects (see, e.g., [1][2][3][4][5][6][7][8][9][10][11] and the references therein). Equations of this type are frequently called also complex Ginzburg-Landau equations.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions to a family of nonlinear Schrödinger equations

Vassilev

2023

J. Phys.: Conf. Ser.

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Section: Introductionmentioning

confidence: 99%

Exact solutions to a family of nonlinear Schrödinger equations

Vassilev

2023

J. Phys.: Conf. Ser.

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“…Beyond the simulation of linear condensed matter systems, the simulation of complex networks processes such as search algorithms has also been proposed through the use of non-linear circuit elements. [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Sahin

Siu

Rafi-Ul-Islam

et al. 2022

Preprint

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Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit’s parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits (TEs) such as 1D and 2D Su–Schrieffer–Heeger (SSH) circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite LC circuits. Through the method of images, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.

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“…The modulational instability (MI) of a constant-amplitude continuous-wave (CW) background against long-wavelength perturbations is a fundamental phenomenon in nonlinear physics [1][2][3][4]. It triggers complex dynamics in water waves [1,2,5], plasmas [6][7][8], electric transmission lines [9,10], nonlinear optics [11]- [23], matter waves [24]- [39], and other physical media [40,41]. In particular, MI initiates the spontaneous production of self-sustained states, such as soliton trains, breathers, and rogue waves (RWs) [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”

mentioning

confidence: 99%

Time-localized solitons generated by zero-wavenumber-gain modulational instability

Liu¹,

Sun²,

Malomed³

et al. 2023

Preprint

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In this work we report on the emergence of a novel type of solitary waves, viz., time-localized solitons in integrable and non-integrable variants of the massive Thirring models and in the threewave resonant-interaction system, which are models broadly used in plasmas, nonlinear optics and hydrodynamics. An essential finding is that the condition for the existence of time-localized dark solitons, which develop density dips in the course of time evolution, in these models coincides with the condition for the occurrence of the zero-wavenumber-gain (ZWG) modulational instability (MI). Systematic simulations reveal that, whenever the ZWG MI is present, patterns reminiscent of such solitons are generically excited from a chaotic background field as fragments within more complex patterns.

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Ginzburg–Landau models of nonlinear electric transmission networks

Cited by 52 publications

References 326 publications

Exact solutions to a family of nonlinear Schrödinger equations

Exact solutions to a family of nonlinear Schrödinger equations

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Time-localized solitons generated by zero-wavenumber-gain modulational instability

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