Dynamical property of interaction solutions to the Chafee-Infante equation via NMSE method.

In this work, we study the Chafee-Infante model with conformable fractional derivative. This model describes the energy balance between equator and pole of solar system, which transmit energy via heat diffusion. To explore the multi soliton solutions and their interaction, we implemented the new modified simple equation (NMSE) scheme. Under some conditions, the obtained solutions are trigonometric, hyperbolic, exponential and their combine form. Only the proposed technique can be provided the solution in terms of trigonometric and hyperbolic form together directly. The periodic, solitary wave and novel interaction of such solitary and sinusoidal solutions has also been established and discussed analytically. For the special values of the existing free parameter, some novel waveforms are existed for the proposed model including, periodic solution, double periodic wave solution, multi-kink solution. The behavior of the obtained solutions is presented in 3-D plot, density plot and counter plot with the help of computational software Maple 18.

Bifurcation, chaos, and stability analysis to the second fractional WBBM model.

This manuscript investigates bifurcation, chaos, and stability analysis for a significant model in the research of shallow water waves, known as the second 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model. The dynamical system for the above-mentioned nonlinear structure is obtained by employing the Galilean transformation to fulfill the research objectives. Subsequent analysis includes planar dynamic systems techniques to investigate bifurcations, chaos, and sensitivities within the model. Our findings reveal diverse features, including quasi-periodic, periodic, and chaotic motion within the governing nonlinear problem. Additionally, diverse soliton structures, like bright solitons, dark solitons, kink waves, and anti-kink waves, are thoroughly explored through visual illustrations. Interestingly, our results highlight the importance of chaos analysis in understanding complex system dynamics, prediction, and stability. Our techniques' efficiency, conciseness, and effectiveness advance our understanding of this model and suggest broader applications for exploring nonlinear systems. In addition to improving our understanding of shallow water nonlinear dynamics, including waveform features, bifurcation analysis, sensitivity, and stability, this study reveals insights into dynamic properties and wave patterns.

Analyzing bifurcation, stability, and wave solutions in nonlinear telecommunications models using transmission lines, Hamiltonian and Jacobian techniques.

This study presents a comprehensive analysis of a nonlinear telecommunications model, exploring bifurcation, stability, and wave solutions using Hamiltonian and Jacobian techniques. The investigation begins with a thorough examination of bifurcation behavior, identifying critical points and their stability characteristics, leading to the discovery of diverse bifurcation scenarios. The stability of critical points is further assessed through graphical and numerical methods, highlighting the sensitivity to parameter variations. The study delves into the derivation of both numerical and analytical wave solutions, aligning them with energy orbits depicted in phase portraits, revealing a spectrum of wave behaviors. Additionally, the analysis extends to traveling wave solutions, providing insights into wave propagation dynamics. Notably, the study underscores the efficacy of the planar dynamical approach in capturing system behavior in harmony with phase portrait orbits. The findings have significant implications for telecommunications engineers and researchers, offering insights into system behavior, stability, and signal propagation, ultimately advancing our understanding of complex nonlinear dynamics in telecommunications networks.

Bifurcation analysis and new waveforms to the first fractional WBBM equation.

This research focuses on bifurcation analysis and new waveforms for the first fractional 3D Wazwaz-Benjamin-Bona-Mahony (WBBM) structure, which arises in shallow water waves. The linear stability technique is also employed to assess the stability of the mentioned model. The suggested equation's dynamical system is obtained by applying the Galilean transformation to achieve our goal. Subsequently, bifurcation, chaos, and sensitivity analysis of the mentioned model are conducted by applying the principles of the planar dynamical system. We obtain periodic, quasi-periodic, and chaotic behaviors of the mentioned model. Furthermore, we introduce and delve into diverse solitary wave solutions, encompassing bright soliton, dark soliton, kink wave, periodic waves, and anti-kink waves. These solutions are visually presented through simulations, highlighting their distinct characteristics and existence. The results highlight the effectiveness, brevity, and efficiency of the employed integration methods. They also suggest their applicability to delving into more intricate nonlinear models emerging in modern science and engineering scenarios. The novelty of this research lies in its detailed analysis of the governing model, which provides insights into its complex dynamics and varied wave structures. This study also advances the understanding of nonlinear wave properties in shallow water by combining bifurcation analysis, chaotic behavior, waveform characteristics, and stability assessments.

A variety of soliton solutions of time M-fractional: Non-linear models via a unified technique.

This work explores diverse novel soliton solutions of two fractional nonlinear models, namely the truncated time M-fractional Chafee-Infante (tM-fCI) and truncated time M-fractional Landau-Ginzburg-Higgs (tM-fLGH) models. The several soliton waves of time M-fractional Chafee-Infante model describe the stability of waves in a dispersive fashion, homogeneous medium and gas diffusion, and the solitary waves of time M-fractional Landau-Ginzburg-Higgs model are used to characterize the drift cyclotron movement for coherent ion-cyclotrons in a geometrically chaotic plasma. A confirmed unified technique exploits soliton solutions of considered fractional models. Under the conditions of the constraint, fruitful solutions are gained and verified with the use of the symbolic software Maple 18. Keeping special values of the constraint, this inquisition achieved kink shape, the collision of kink type and lump wave, the collision of lump and bell type, periodic lump wave, bell shape, some periodic soliton waves for time M-fractional Chafee-Infante and periodic lump, and some diverse periodic and solitary waves for time M-fractional Landau-Ginzburg-Higgs model successfully. The required solutions in this work have many constructive descriptions, and corporal behaviors have been incorporated through some abundant 3D figures with density plots. We compare the m-fractional derivative with the beta fractional derivative and the classical form of these models in two-dimensional plots. Comparisons with others' results are given likewise.

New wave behaviors of the Fokas-Lenells model using three integration techniques.

In this investigation, we apply the improved Kudryashov, the novel Kudryashov, and the unified methods to demonstrate new wave behaviors of the Fokas-Lenells nonlinear waveform arising in birefringent fibers. Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. These solutions encompass periodic waves with W-shaped profiles, gradually increasing amplitudes, rapidly increasing amplitudes, double-periodic waves, and breather waves with symmetrical or asymmetrical amplitudes. Singular solitons with single and multiple breather waves are also derived. Based on these findings, we can say that our implemented methods are more reliable and useful when retrieving optical soliton results for complicated nonlinear systems. Various potential features of the derived solutions are presented graphically.

Soliton solutions for the Zoomeron model applying three analytical techniques.

The Zoomeron equation is used in various categories of soliton with unique characteristics that arise in different physical phenomena, such as fluid dynamics, laser physics, and nonlinear optics. To achieve soliton solutions for the Zoomeron nonlinear structure, we apply the unified, the Kudryashov, and the improved Kudryashov techniques. We find periodic, breather, kink, anti-kink, and dark-bell soliton solutions from the derived optical soliton solutions. Bright, dark, and bright-dark breather waves are also established. Finally, some dynamic properties of the acquired findings are displayed in 3D, density, and 2D views.

Bifurcation analysis on ion sound and Langmuir solitary waves solutions to the stochastic models with multiplicative noises.

This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.

Trends and patterns of inequalities in using facility delivery among reproductive-age women in Bangladesh: a decomposition analysis of 2007-2017 Demographic and Health Survey data.

OBJECTIVES: The prime objectives of the study were to measure the prevalence of facility delivery, assess socioeconomic inequalities and determine potential associated factors in the use of facility delivery in Bangladesh.DesignCross-sectional. SETTING: The study involved investigation of nationally representative secondary data from the Bangladesh Demographic and Health Survey between 2007 and 2017-2018. PARTICIPANTS: The participants of this study were 30 940 (weighted) Bangladeshi women between the ages of 15 and 49. METHODS: Decomposition analysis and multivariable logistic regression were both used to analyse data to achieve the study objectives. RESULTS: The prevalence of using facility delivery in Bangladesh has increased from 14.48% in 2007 to 49.26% in 2017-2018. The concentration index for facility delivery utilisation was 0.308 with respect to household wealth status (p<0.001), indicating that use of facility delivery was more concentrated among the rich group of people. Decomposition analysis also indicated that wealth quintiles (18.31%), mothers' education (8.78%), place of residence (7.75%), birth order (5.56%), partners' education (4.30%) and antenatal care (ANC) seeking (8.51%) were the major contributors to the prorich socioeconomic inequalities in the use of facility delivery. This study found that women from urban areas, were overweight, had any level of education, from wealthier families, had ANC, and whose partners had any level of education and involved in business were more likely to have facility births compared with their respective counterparts. CONCLUSIONS: This study found a prorich inequality in the use of facility delivery in Bangladesh. The socioeconomic disparities in facility delivery must be addressed if facility delivery usage is to increase in Bangladesh.

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models.

This study presents a modification form of modified simple equation method, namely new modified simple equation method. Multiple waves and interaction of soliton solutions of the Phi-4 and Klein-Gordon models are investigated via the scheme. Consequently, we derive various novels and more general interaction, and multiple wave solutions in term of exponential, hyperbolic, and trigonometric, rational function solutions combining with some free parameters. Taking special values of the free parameters, interaction of two dark bells, interaction of two bright bells, two kinks, two periodic waves, kink and soliton, kink-rogue wave solutions are obtained which is the key significance of this method. Properties of the achieved solutions have many useful descriptions of physical behavior, correlated to the solutions are attained in this work through plentiful 3D figures, density plot and 2D contour plots. The results derived may increase the prospect of performing significant experimentations and carry out probable applications.