The discrete tanh method for solving the nonlinear differential-difference equations

Houwe, Alphonse; Doka, Serge Y.; Acay, Bahar; Hoan, Luu Vu Cam

doi:10.1142/s0217979220501775

Cited by 24 publications

(6 citation statements)

References 27 publications

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“…MI [29][30][31][32][33][34][35] is one of the most important study which lies to the event of exponential growth of small disturbances related on a CW. In fiber-optic, MI is well known in the case of ultrashort pulse propagation and it has been investigated with diverse optical soliton.…”

Section: Modulation Instability Gain Spectrummentioning

confidence: 99%

“…The presence of the nonlinearity associated with the dispersion terms could undoubtedly let appear the MI to study the associated spectrum gain in order to determine the instability states of the solitons obtained. The MI [29][30][31][32][33][34][35] and solitons are strongly associated due the generation of trains of perfect soliton. The MI is also known as an epiphenomenon when small perturbations increase during the confrontation between dispersion and nonlinearity terms In this paper, it is used the dimensionless form of the CNLSE for magneto-optic waveguides with parabolic law nonlinearity given by [5,8,13]…”

Section: Introductionmentioning

confidence: 99%

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Miscellaneous optical solitons in magneto-optic waveguides associated to the influence of the cross-phase modulation in instability spectra

Abbagari¹,

Houwe²,

Mukam³

et al. 2021

Phys. Scr.

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By employing the traveling-wave hypothesis to the coupled nonlinear Schrödinger equation (CNLSE), the constraint relation on metamaterials parameters and the auxiliary equation have been recovered successfully. Conjecturing the values of the coefficients of the auxiliary equation, a diversity of solutions have been constructed while respecting the conditions of existence of these solutions. By choosing adequate parameters, it is obtained W-shape bright, dark, kink, anti-kink like optical solitons for the CNLSE which controls waves in magneto-optic waveguides in the presence of cross-phase modulation (XMP). To deal with the influence of the XMP to Modulation Instability (MI), the linearization technique was adopted and the continuous wave (CW) solutions were used to obtaining the dispersion relation as well as the associated MI gain spectrum. The study of the MI gain spectrum have been done in the normal and anomalous dispersive regimes associated with zero-birefringence, linear-birefringence and circular birefringence. The MI gain spectrum curves illustrating the miscellaneous of optical solitons in the magneto-optic waveguides were obtained. It is noted that these results sufficiently illustrate the dynamic of the nonlinear optic fibers through the 3D and 2D spatiotemporal plot evolutions.

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Section: Modulation Instability Gain Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Miscellaneous optical solitons in magneto-optic waveguides associated to the influence of the cross-phase modulation in instability spectra

Abbagari¹,

Houwe²,

Mukam³

et al. 2021

Phys. Scr.

Self Cite

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“…en, Acay and Inc [15] proposed the temperature dynamics of a building and examined this model which has a crucial place in daily life. In 2020, Houwe et al [16] investigated analytical solutions for the nonlinear differential-difference equations (DDEs) having fractional-order derivatives and employed the discrete tanh method in computations. As well, Akinlar et al [17] considered an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations, generated a new SIRS model and perturbed it to the fractional-stochastic systems, and studied chaotic behavior at disease-free and endemic steady-state points on these systems.…”

Section: Introductionmentioning

confidence: 99%

The Impact of the SARS-CoV-2 Epidemic on World Indices: The Entropy Approach

Karakaş

Doğan

Çalik

2021

Mathematical Problems in Engineering

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The coronavirus disease (COVID-19) outbreak started in December 2019 in Wuhan. The virus has spread around the whole world, and it has caused a strong and serious pandemic. Symptoms such as cough, respiratory distress, diarrhea, and fatigue associated with COVID-19 are typical clinical findings. Coronavirus infection has become an important public health concern because of its increasing prevalence, serious complications, and mortality. In light of this information, we examine different entropy methods for world indices (ISE 30, FTSE 100, NIKKEI 225, SP 500, and DAX 30) in the pre-COVID-19 period (02.01.2019–17.11.2019) and the post-COVID-19 period (18.11.2019–23.11.2020) in this article. Besides, we discuss the performances of entropies such as Shannon, Renyi, Tsallis, and approximate entropy (ApEn) in detail and perform the notion of entropy for volatility measure. As a result, we present the numerical results for the data set.

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“…Then, Acay and Inc [13] proposed non-local singular fractional operators and examined this model, which has a very important place in everyday life. In 2020, Houwe et al [14] studied analytical solutions of nonlinear differential equations (DED) with fractional derivatives and used the discrete tanh method for the calculations. In addition, Akinlar et al [15] take an epidemic system with additional fractional white noise, build a new SIRS model and mix it into the fractional model, to show that epidemics can be modeled more competently in fractionalstochastic environments than those modeled by fractionalstochastic environments.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Conditional Dependence for Turkey Earthquake Data: CD Vine Copula Approach

Karakaş

Demir

Çalik

2021

Bitlis Eren University Journal of Science and Technology

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The objective of this research was to use Turkey's major fault zones, which are located on fault lines, to describe the dependency structure. The current study also intended to show the dynamic structure of the conditional dependencies of the earthquake data in Turkey in terms of depth and magnitude, using the CD-vine copula method. Conditional dependence, also known as the CD-vine method, makes obtaining a complex dependency structure simpler. The current research uses 30 years of data from the Eastern Anatolian Fault line and the North Anatolian Fault line to describe the dynamic conditional dependency structure. As a consequence, this dependency structure is represented graphically and numerically in tables and graphs.

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The discrete tanh method for solving the nonlinear differential-difference equations

Cited by 24 publications

References 27 publications

Miscellaneous optical solitons in magneto-optic waveguides associated to the influence of the cross-phase modulation in instability spectra

Miscellaneous optical solitons in magneto-optic waveguides associated to the influence of the cross-phase modulation in instability spectra

The Impact of the SARS-CoV-2 Epidemic on World Indices: The Entropy Approach

Dynamic Conditional Dependence for Turkey Earthquake Data: CD Vine Copula Approach

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