IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v201y2022icp254-274.html

Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes

Author

Listed:
  • Kumar, Sachin
  • Kumar, Amit

Abstract

In this present paper, we obtain hyperbolic, exponential, trigonometric function, other soliton solutions, and their combinations for the cold bosonic atoms in a zig-zag optical lattice model based on two efficient methods, such as the generalized Riccati equation mapping (GREM) method and generalized Kudryashov (GK) method. The used techniques are very reliable and effective tools and provide numerous exact soliton solutions of the nonlinear PDE. The zig-zag optical lattice model, widely used to represent the nonlinear wave and the soliton dynamics in fluid dynamics and plasma physics, is examined in this article to obtain exact optical soliton solutions and study their physical properties. For this, we first convert a partial differential equation (PDE) into an ordinary differential equation (ODE) by employing wave transformation and then split the equation into imaginary and real parts. The derived optical soliton solutions are illustrated graphically using Mathematica software to distinguish constant parameter values. Consequently, bell-shape, anti-bell-shape, traveling wave, periodic, mix periodic, singular soliton, and some new types of solitons demonstrate to validate these acquired outcomes with physical phenomena and make the results worthy. Furthermore, the 3D, 2D, and contour graphs are sketched to assign suitable constant parameters to illustrate the physical phenomena of the obtained solutions. The accomplished soliton solutions indicate that the applied computational system is a direct, reliable, productive, and more complex physical phenomenon. Symbolic computation is used in the software package Mathematica to obtain the various soliton solutions and different dynamical behavior of the newly formed solutions

Suggested Citation

  • Kumar, Sachin & Kumar, Amit, 2022. "Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 254-274.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:254-274
    DOI: 10.1016/j.matcom.2022.05.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422001975
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.05.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
    2. Zhu, Shun-dong, 2008. "The generalizing Riccati equation mapping method in non-linear evolution equation: application to (2+1)-dimensional Boiti–Leon–Pempinelle equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1335-1342.
    3. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kazmi, Syeda Sarwat & Jhangeer, Adil & Riaz, Muhammad Bilal, 2026. "Data-driven approach to shallow water equation in ocean engineering: Multi-soliton solutions, chaos, and sensitivity analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 573-595.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Seadawy, Aly R. & Ali, Asghar & Althobaiti, Saad & Sayed, Samy, 2021. "Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Pengbo Wan & Jalil Manafian & Hajar Farhan Ismael & Sizar Abid Mohammed, 2020. "Investigating One‐, Two‐, and Triple‐Wave Solutions via Multiple Exp‐Function Method Arising in Engineering Sciences," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    3. J. Muhammad & U. Younas & Haroon & H. Mukalazi & M. E. Meligy & K. A. Alnowibet, 2025. "On the Study of Nonlinear Murray Equation in Non‐Newtonian Fluids: Fractional Solitary Wave Structures, Chaos, and Sensitivity Demonstration," Advances in Mathematical Physics, John Wiley & Sons, vol. 2025(1).
    4. Devi, Munesh & Yadav, Shalini & Arora, Rajan, 2021. "Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    5. Hashemi, M.S., 2018. "Invariant subspaces admitted by fractional differential equations with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 161-169.
    6. Saleh Alshammari & Othman Abdullah Almatroud & Mohammad Alshammari & Hamzeh Zureigat & M. Mossa Al-Sawalha, 2024. "Exploring Kink Solitons in the Context of Klein–Gordon Equations via the Extended Direct Algebraic Method," Mathematics, MDPI, vol. 12(21), pages 1-29, November.
    7. Alvaro H. Salas, 2012. "Solving Nonlinear Partial Differential Equations by the sn‐ns Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Lijun Zhang & C. M. Khalique, 2014. "Traveling Wave Solutions and Infinite‐Dimensional Linear Spaces of Multiwave Solutions to Jimbo‐Miwa Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Li, Hui & Li, Ye-Zhou, 2018. "Meromorphic exact solutions of two extended (3+1)-dimensional Jimbo–Miwa equations," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 369-375.
    10. Hasibun Naher & Farah Aini Abdullah, 2012. "New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)‐Dimensional Evolution Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    11. Bashir, Azhar & Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R., 2022. "The Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    12. El-Ganaini, Shoukry & Kumar, Sachin, 2023. "Symbolic computation to construct new soliton solutions and dynamical behaviors of various wave structures for two different extended and generalized nonlinear Schrödinger equations using the new improved modified generalized sub-ODE proposed method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 28-56.
    13. Xiaomin Wang & Sudao Bilige & Jing Pang, 2020. "Rational Solutions and Their Interaction Solutions of the (3 + 1)‐Dimensional Jimbo‐Miwa Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    14. Biswas, Swapan & Ghosh, Uttam & Raut, Santanu, 2023. "Construction of fractional granular model and bright, dark, lump, breather types soliton solutions using Hirota bilinear method," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    15. Xie, Xiao-Ran & Zhang, Run-Fa, 2025. "Neural network-based symbolic calculation approach for solving the Korteweg–de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    16. Qing Meng & Bin He, 2016. "Bounded Traveling Wave Solutions and Their Relations for the Generalized HD Type Equation," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    17. Hongwei Yang & Yong Zhang & Xiaoen Zhang & Xin Chen & Zhenhua Xu, 2016. "The Rational Solutions and Quasi‐Periodic Wave Solutions as well as Interactions of N‐Soliton Solutions for 3 + 1 Dimensional Jimbo‐Miwa Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    18. Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    19. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    20. Hayman Thabet & Subhash Kendre & Dimplekumar Chalishajar, 2017. "New Analytical Technique for Solving a System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-15, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:254-274. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.