Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability

Chen, Yue; Lu, Dianchen; Arshad, Muhammad; Nasreen, Naila; Qian, Xiaoyong

doi:10.3390/e22020202

“…This work addresses new shape of the chirped bright and dark soliton solutions through the CGLE by using the new sub-ODE equations. By using a special ansatz of the traveling wave transformation, we obtain a new shape of the chirp comparatively to the previous works reported in literature [26,[31][32][33][34]36,45]. In addition, new singular soliton solutions, trigonometric function solutions and complex traveling waves have been obtained.…”

Section: Discussionmentioning

confidence: 68%

“…In our knowledge, these results are new compared to Refs. [28][29][30][31][32][33][34], and are going to be helpful to explain physical phenomena.…”

mentioning

confidence: 99%

New shape of the chirped bright, dark optical solitons and complex solutions for (2+1) Ginzburg-Landau equation

Houwe

¹

,

Băleanu²,

Rezazadeh³

et al. 2021

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Investigation of the Ginzburg-Landau equation (GLE) was done to secure new chirped bright, dark periodic and singular function solutions. For this, we used the traveling wave hypothesis and the chirp component. From there it was pointed out the constraint relation to the dierent arbitrary parameters of the GLE. Thereafter, we employed the improved sub-ODE method to handle the nonlinear ordinary differential equation (NODE). It was highlighted the virtue of the used analytical method via new chirped solitary waves. In our knowledge, these results are new, and will be helpful to explain physical phenomenons.

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“…In this article we present the clean experimental realization of nontransient, long lifetime (10,000s of round trips) complex dynamical behaviors for SWE bright and dark solitary waves propagating within in an AFR. 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].…”

Section: Introductionmentioning

confidence: 68%

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

Anderson,

Janantha,

Alcala

et al. 2020

Preprint

0

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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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“…In this article we present the clean experimental realization of nontransient, long lifetime (tens of thousands of round trips) complex dynamical behaviors for SWE bright and dark solitary waves propagating within an AFR. These results are distinct from the study of dissipative solitons in the above systems where the focus has been on exploring transient behaviors, periodic modulations and isolating extreme events [41][42][43][44]. 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 [45].…”

Section: Introductionmentioning

confidence: 68%

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

Anderson

¹

,

Janantha²,

Alcala³

et al. 2022

New J. Phys.

3

0

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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 self-generated microwave spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide. The waveguide is operated in a ring geometry in which the net losses are directly compensated for via linear amplification on each round trip (of the order of 100~ns). These behaviors exhibit periods ranging from tens to thousands of round trip times (of the order of $\mu$s) and are stable for 1000s of periods (of the order of~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. All observed behaviors are robust over wide parameter regimes, making them promising for technological applications. We present ten experimental observations which span all categories of dynamical behavior previously theoretically predicted to be observable. This represents 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. The reported dynamical pattern formation of self-generated dark solitary waves in attractive nonlinearity without external sources or potentials, however, is entirely novel and is presented for both the periodic breather and complex recurrence behaviors.

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Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg–Landau Dynamical Equation with Applications and Stability

Cited by 9 publications

References 39 publications

New shape of the chirped bright, dark optical solitons and complex solutions for (2+1) Ginzburg-Landau equation

New shape of the chirped bright, dark optical solitons and complex solutions for (2+1) Ginzburg-Landau equation

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

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

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