Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

Iqbal, Sayed Allamah; Hafez, M. G.; Uddin, Mesbah

doi:10.1007/s40314-021-01753-7

Cited by 21 publications

(12 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the wavelength (frequency) are shorter (increasing) with the increase of both BFD and CFD parameter. 3 that for different choice of arbitrary parameters, one can produce unstable soliton, that is, rouge waves for fractional value of the parameter μ from Equation (38) and Equation ( 39), but it would always produce singular soliton for μ = 1. The amplitudes of rouge waves are increasing with regard to increase of fractional parameter, but decreasing and behaves pulse like with the increasing values of time.…”

Section: Graphical Representations and Discussionmentioning

confidence: 99%

“…The development of BFD and CFD meet many features of fundamental calculus, whereas the earlier fractional derivatives does not support some features of fundamental calculus. In References [33][34][35][36][37][38], authors have been used such derivatives for describing a wide range of physical processes. For instance, Uddin et al [33][34][35][36] have reported that the effect of BFD parameter on nonlinear wave phenomena by considering different kinds of environments.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Uddin et al [33][34][35][36] have reported that the effect of BFD parameter on nonlinear wave phenomena by considering different kinds of environments. Hafez et al [37] and Iqbal et al [38] have reported that the effect of CFD parameter on wave phenomena with their dynamical features in optical bullets and one-dimensional nonlinear electrical transmission line, respectively. It is now required to investigate nonlocal and nonconservative physical issues in optical fibers due to imperfections/nonuniformities in birefringent fibres along with some technical challenges resulting from fiber technologies discussed previously.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

Uddin

Hafez

2022

Advances in Mathematical Physics

Self Cite

View full text Add to dashboard Cite

The work explores the optical wave solutions along with their graphical representations by proposing the coupled spatial-temporal fractional cubic-quartic nonlinear Schrödinger equation with the sense of two fractal derivatives (beta and conformable derivative) and Kerr law nonlinearity for birefringent fibers. The new extended direct algebraic method for the first time is implemented to achieve this goal. Many optical solutions are listed along with their existence criteria. Based on the existence criteria, the cubic-quartic bright, and singular optical soliton, periodic pulse, and rouge wave profiles are supported in birefringent fibers with the influence of both beta and conformable derivative parameter.

show abstract

Section: Graphical Representations and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

Uddin

Hafez

2022

Advances in Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is worth noting that the dynamic system method is also an effective method for constructing traveling wave solutions [35][36][37][38][39][40]. The idea of this method is that: (1) establish a plane dynamics system, (2) integrate various trajectories, (3) obtain all possible exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation, chaotic pattern and traveling wave solutions for the fractional Bogoyavlenskii equation with multiplicative noise

Han,

Jiang

2024

Phys. Scr.

View full text Add to dashboard Cite

This paper presents a new study that incorporates the Stratonovich integral and conformal fractional derivative into the fractional stochastic Bogoyavlenskii equation with multiplicative noise. The study exposes the behavior of the system, including sensitivity, chaos and traveling wave solutions, by using the planar dynamical systems approach. Time series, periodic perturbation, phase portraits, and the Poincar'{e} section are used to comprehensively study the dynamic properties. Notably, the research uses the planar dynamic systems method to build multiple traveling wave solutions, including kink wave, dark soliton, and double periodic solutions. Furthermore, a comparative study approach is applied to investigate the effects of fractional derivative and multiplicative noise on the traveling wave solutions, which demonstrate a significant influence of both variables. This work demonstrates the creative application of the planar dynamic system method to the analysis of nonlinear wave equations, offering insightful information that may be generalized to more complex wave phenomena.

show abstract

“…Examples include radioactive decay, spring-mass systems, population growth, and predator-prey models. As nonlinear model, KdV equations has enormous efect on many aspects in theoretical and mathematical physics [11], quantum and string theory [12,13]. KdV equations are famous for capturing nonlinear dispersive waves.…”

Section: Introductionmentioning

confidence: 99%

Constructing and Predicting Solutions for Different Families of Partial Differential Equations: A Reliable Algorithm

Qayyum

Khan

2022

Journal of Mathematics

View full text Add to dashboard Cite

The construction of mathematical models for different phenomena, and developing their solutions, are critical issues in science and engineering. Among many, the Buckmaster and Korteweg-de Vries (KdV) models are very important due to their ability of capturing different physical situations such as thin film flows and waves on shallow water surfaces. In this manuscript, a new approach based on the generalized Taylor series and residual function is proposed to predict and analyze Buckmaster and KdV type models. This algorithm estimates convergent series with an easy-to-use way of finding solution components through symbolic computation. The proposed algorithm is tested against the Buckmaster and KdV equations, and the results are compared with available solutions in the literature. At first, proposed algorithm is applied to Buckmaster-type linear and nonlinear equations, and attained the closed-form solutions. In the next phase, the proposed algorithm is applied to highly nonlinear KdV equations (namely, classical, modified, and generalized KdV) and approximate solutions are obtained. Simulations of the test problems clearly reassert the dominance and capability of the proposed methodology in terms of accuracy. Analysis reveals that the projected scheme is reliable, and hence, can be utilized for more complex problems in engineering and the sciences.

show abstract

Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

Cited by 21 publications

References 39 publications

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

Optical Wave Phenomena in Birefringent Fibers Described by Space-Time Fractional Cubic-Quartic Nonlinear Schrödinger Equation with the Sense of Beta and Conformable Derivative

Bifurcation, chaotic pattern and traveling wave solutions for the fractional Bogoyavlenskii equation with multiplicative noise

Constructing and Predicting Solutions for Different Families of Partial Differential Equations: A Reliable Algorithm

Contact Info

Product

Resources

About