Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques

Faridi, Waqas Ali; Asjad, Muhammad Imran; Toseef, Muhammad; Amjad, Taha

doi:10.1007/s11082-022-04179-5

Cited by 17 publications

(2 citation statements)

References 36 publications

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“…The behavior of the system over space (x) and time (t) is reflected in the real wave function, u(x, t), which varies. This article explores the Kairat-II equation [32] model using innovative techniques, including the extended direct algebraic method [33][34][35][36]. Recently, Awadalla et al [37] developed the exact solutions of Kairat-II equation by utilizing the Expa function method, modified simplest equation and the generalized Kudryashov methods and obtained trigonometric, hyperbolic trigonometric and exponential functions solutions, but they did not discuss the hyper-trigonometric, rational and other generalized soliton types.…”

Section: Introductionmentioning

confidence: 99%

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

Faridi,

Tipu,

Myrzakulova

et al. 2024

Phys. Scr.

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This study investigates the Kairat-II equation, describing optical pulse behavior in opticalfibers and plasma. To uncover new solitary wave profiles, the study employs an extendeddirect algebraic method. Prior to this study, no previous research has achieved solutions ofthis kind. This innovative approach efficiently encompasses a comprehensive set of thirty-sevensolitonic wave profiles, spanning various soliton families. The investigation unveils novel solitonicwave patterns, including plane solutions, hyper-geometric solutions, mixed hyperbolic solutions,periodic and mixed periodic solutions, mixed trigonometric solutions, trigonometric solutions,shock solutions, mixed shock singular solutions, mixed singular solutions, complex solitary shock solutions, singular solutions, and shock wave solutions. To demonstrate the pulse propagationcharacteristics, the research presents 2-D, 3-D, and contour graphics based on parameter values,aiding in a better understanding of the phenomenon.

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Section: Introductionmentioning

confidence: 99%

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

Faridi,

Tipu,

Myrzakulova

et al. 2024

Phys. Scr.

Self Cite

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“…These methods are given in (Malfliet 1992;Fan 2000a, b;Elwakil et al 2002;Chen and Zhang 2004;Fu et al 2001;Shen and Pan 2003;Chen and Hong-Qing 2004;Chen and Yan 2006;Wang et al 2008;Guo and Zhou 2010;Lü et al 2010;Li et al 2010;Manafian 2016;Khater 2015;Youssoufa et al 2019;Youssoufa et al 2022). Many researchers have applied such methods to various equations, (Khater and Zahran 2016;Wazwaz 2007;Manafian et al 2017;Mirzazadeh et al 2015;Wazwaz and Mehanna 2021;Biswas, Aceves et al 2001;Singh et al 2020;El-Ganaini et al 2015;Ali Faridi et al 2024;Ali Faridi and AlQahtani 2023;Ali Faridi et al 2023;Ali Faridi et al 2023a;Ali Faridi et al 2023b;Zain Majida et al 2023;Hamza Rafiq et al 2023;Kaplan et al 2018;Shakeel et al 2014;Ahmad and Mustafa 2023;Hussain Tipu et al 2024;Rani et al 2022;Rani et al 2020;Aniqa and Ahmad 2022;Ali et al 2023a, b;Ali et al 2023c;Wazwaz and Triki 2010;Khater and Z...…”

Section: Introductionmentioning

confidence: 99%

Some optical solitons and modulation instability analysis of (3 + 1)-dimensional nonlinear Schrödinger and coupled nonlinear Helmholtz equations

Alsaud,

Youssoufa,

Inc

et al. 2024

Opt Quant Electron

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In this study, we acquired some optical solitons of (3 + 1) dimensional nonlinear Schrödinger equation (3DNLSE) and coupled nonlinear Helmholtz equations (CNLHE) by using generalized $$\left(\frac{{G}^{\prime}}{G}\right)$$ G ′ G -expansion method (GEM). We are able to derive exponential, trigonometric, and hyperbolic solutions. We notice that Mathematica 11.2 offer the equations for these answers. Aside from that, we display some of the solution’s graphic performance. Recently, accurate traveling-wave solutions for nonlinear partial differential equations (NLPDEs) have been acquired using this technique. Through linear stability analysis, we derive an analytical expression for the instability gain and analyze its main characteristics. Finally, we assess the robustness and stability of the solitary waves through numerical simulations and compare the accuracy of the analytical and numerical results. The obtained ultra-short optical solitons can be widely used as a guide for practical applications in telecommunications domain.

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Analytical insights into cold bosonic atoms in a zigzag optical lattice: Invariant analysis, exact solutions, and bifurcation analysis using phase portraits

Yadav,

Kumar Gupta

2024

Math Methods in App Sciences

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This work delves into the behavior of cold bosonic atoms within a zigzag optical lattice which offers a rich platform for studying quantum many‐body physics and has potential applications in various fields including quantum simulation, quantum computing, and precision measurement. The study aims to derive exact solutions and explore qualitative properties through dynamical analysis. Exact solutions of the nonlinear differential equation model can provide insights into the behavior of bosonic atoms in complex optical lattice configurations, allowing researchers to simulate and study phenomena such as quantum phase transitions, many‐body localization, and exotic states of matter. The invariant analysis has been performed for the first time on the specified equation, yielding a reduced system of equations with forms that are easier to handle. Novel techniques are applied to extract solutions from the reduced system of equations obtained via invariant analysis. The results reveal a rich set of solutions, including various traveling wave solutions and doubly periodic functions in the form of Jacobian elliptic functions. Bifurcation analysis, conducted through phase portraits, provides insights into the system's long‐term behavior under different parameter values. This work contributes to a deeper understanding of the dynamics of cold bosonic atoms in optical lattices via 2D and 3D plots of obtained solutions depicting the change in the behavior of soliton solutions with fractional derivative parameter.

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Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques

Cited by 17 publications

References 36 publications

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

Some optical solitons and modulation instability analysis of (3 + 1)-dimensional nonlinear Schrödinger and coupled nonlinear Helmholtz equations

Analytical insights into cold bosonic atoms in a zigzag optical lattice: Invariant analysis, exact solutions, and bifurcation analysis using phase portraits

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