Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management

Fujioka, Jorge; Cortés, Emilio; Pérez-Pascual, R.; Rodrı́guez, Rogelio; Espinosa, A.; Malomed, Boris A.

doi:10.1063/1.3629985

Cited by 94 publications

(33 citation statements)

References 61 publications

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“…[24][25][26] The VM has been applied in many systems in order to gain a better understanding of the behavior of solitons. [27][28][29][30][31][32][33][34] In fact, in some cases, the stability (or instability) of solitons, or the possibility of having chaotic solutions, can be revealed simply from the form of the ordinary differential equations (ODEs) provided by the VM, without the need to actually solve them. On the other hand, the VK criterion has been useful for estimating the stability of solitons in many cases.…”

Section: Variational Vakhitov-kolokolov Analysismentioning

confidence: 99%

Radiationless Higher-Order Embedded Solitons

Fujioka

Espinosa

2013

J. Phys. Soc. Jpn.

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The soliton solutions of a higher-order nonlinear Schrödinger equation including nonlinearities of orders 2b þ 1 and 4b þ 1, as well as second-and fouth-order dispersive terms, are obtained. It is shown that these solitons may be (or may not be) embedded, depending on the coefficients of the equation. The radiationless character of the embedded solitons is explained by analyzing the Fourier transform of the equation. The stability of these solitons is studied analytically and numerically. In the analytical approach, we combined the Vakhitov-Kolokolov stability criterion with the standard variational method. This combined technique predicts that the standard solitons are unstable and the embedded ones might be stable. The numerical results confirm these predictions, and show that the embedded and standard solitons respond very differently to perturbations.

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Section: Variational Vakhitov-kolokolov Analysismentioning

confidence: 99%

Radiationless Higher-Order Embedded Solitons

Fujioka

Espinosa

2013

J. Phys. Soc. Jpn.

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“…The governing model that describes the propagation of optical solitons and optical soliton complexes (soliton molecules) is the nonlinear Schrdinger's equation (NLSE) that comes with various forms of nonlinearity. A new form of nonlinearity was proposed during 2011, which is called quadratic-cubic (QC) [25]. Thus far, NLSE with QC nonlinearity has been studied, without prerturbation terms, by the aid of some integration algorithms, including the application of semi-inverse variational principle (SVP) [26,31].…”

Section: Introductionmentioning

confidence: 99%

“…In the past, solitons in optical metamaterials have been studied with various forms of non-Kerr laws of nonlinearity where several integration schemes have been implemented [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Interested reader also read herein references [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. This paper is going to revisit the study of solitons in optical metamaterials for a specific form of nonlinear medium.…”

Section: Introductionmentioning

confidence: 99%

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

Foroutan

Manafian

2018

J. Eur. Opt. Soc.-Rapid Publ.

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Background: This paper studies soliton perturbation in optical metamaterials, with anticubic nonlinearity. Methods: Two integration approaches, namely, the extended trial equation method (ETEM) and the improved G'/Gexpansion method (IGEM) are presented. Results: Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also demonstrated. All solutions have been verified back into its corresponding equation with the aid of maple package program. Conclusions: Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in optical metamaterials.

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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]. …”

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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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Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management

Cited by 94 publications

References 61 publications

Radiationless Higher-Order Embedded Solitons

Radiationless Higher-Order Embedded Solitons

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

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

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