Tree-like structures and Freak waves generation induced by quintic-nonlinearity and cubic-Raman effect in a nonlinear metamaterial

Nnanga, Bibiane Mireille Ndi; Dontsop, Paul Yannick Gouadjio; Essama, Bedel Giscard Onana; Shabat, Mohammed M.; Yémélé, David; Atangana, Jacques

doi:10.1007/s11082-020-02469-4

Cited by 10 publications

(21 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is important to note that there exist three regimes in a nonlinear metamaterial. [ 47 ] These regimes cannot come into play simultaneously in the optical system. So, they occur alternatively.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

“…In addition to that the nonlinear metamaterial will alternatively exhibit three regimes known as the “positive index regime,” “NIR,” and “AR”. [ 47 ] The nature of each regime is determined by the refractive index (

n = n' + i n ″

), which is the main parameter allowing ome to control light interactions with matter. [ 37,48 ] Two cases are outlined.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Essama

Essiane

Biya-Motto

et al. 2020

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

Herein, the behavior of the soliton light pulse when quintic –nonlinearity, third‐order dispersion, and self‐steepening come into play in a nonlinear metamaterial for both negative index and absorption regimes is presented. The collective coordinate technique is used with the conventional Gaussian ansatz function to give a good characterization of the pulse profile. In addition to that the ansatz function presents six coordinates describing the internal behavior of the pulse during the propagation. Furthermore, the main goal of this work is to give an exact measure of the internal behavior leading to the generation of rogue events by collective coordinates. Some interesting results are found when the aforementioned linear and nonlinear effects gradually come into play. Among them is the generation of different forms of breather solutions, divergent wave trains, different forms of Sasa–Satsuma rogue waves, parabolic wave trains, Peregrine rogue waves, and “tree structures”. Some special phenomena known as deletion, translation, attenuation, and wall of waves are also shown. However, some new exact rogue solutions of the cubic–quintic nonlinear Schrödinger equation are also found.

show abstract

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

n = n' + i n ″

), which is the main parameter allowing ome to control light interactions with matter. [ 37,48 ] Two cases are outlined.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Essama

Essiane

Biya-Motto

et al. 2020

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

show abstract

“…It appears when a chaotic waves field is generated by modulation instability. This expanding structure corresponds to the so-called "tree structure" [24]. Some investigations have been done in literature concerning this phenomenon.…”

Section: Introductionmentioning

confidence: 96%

“…Such phenomenology has been firstly observed and extensively analyzed in [26], which is related to the umbilical gradient catastrophe. It has been also shown that Raman effect can induce the appearance of particular "tree structure" with roots which can be called "roots of propagation" [24] [27]. Authors else such as Dudley [28], sustains that such "tree structures" correspond to signatures of analytic nonlinear Schrödinger equation solutions in chaotic modulation instability [24].…”

Section: Introductionmentioning

confidence: 98%

“…It has been also shown that Raman effect can induce the appearance of particular "tree structure" with roots which can be called "roots of propagation" [24] [27]. Authors else such as Dudley [28], sustains that such "tree structures" correspond to signatures of analytic nonlinear Schrödinger equation solutions in chaotic modulation instability [24]. Furthermore, to the best of our knowledge, the characterization of electromagnetic wave behavior, the description of internal excitation leading to specific rogue waves generation, the so-called tree structures corresponding to rogue events signature in a chameleon transmission line, have been least reported.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line

Essama¹,

Essiane²,

Biya-Motto³

et al. 2020

JAMP

Self Cite

View full text Add to dashboard Cite

We analyze the particular behavior exhibited by a chaotic waves field containing Peregrine soliton and Akhmediev breathers. This behavior can be assimilated to a tree with "roots of propagation" which propagate randomly. Besides, this strange phenomenon can be called "tree structures". So, we present the collapse of dark and bright solitons in order to build up the above mentioned chaotic waves field. The investigation is done in a particular nonlinear transmission line called chameleon nonlinear transmission line. Thus, we show that this line acts as a bandpass filter at low frequencies and the impact of distance, frequency and dimensionless capacitor are also presented. In addition, the chameleon's behavior is due to the fact that without modifying the appearance structure, it can present alternatively purely right-or left-handed transmission line. This line is different to the composite one.

show abstract

Breathers-like rogue wave trains induced by nonlinear dynamics of DNA breathing

Essama¹,

Bisse²,

Essiane³

et al. 2022

Appl. Phys. A

View full text Add to dashboard Cite

Tree-like structures and Freak waves generation induced by quintic-nonlinearity and cubic-Raman effect in a nonlinear metamaterial

Cited by 10 publications

References 72 publications

Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line

Breathers-like rogue wave trains induced by nonlinear dynamics of DNA breathing

Contact Info

Product

Resources

About