IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v219y2024icp473-490.html
   My bibliography  Save this article

Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation

Author

Listed:
  • Mann, Nikita
  • Rani, Setu
  • Kumar, Sachin
  • Kumar, Raj

Abstract

A nonlinear electrical lattice is an effective experimental tool for dealing with nonlinear dispersive media and creating possibilities for the realistic modeling of electrical soliton. In this work, we discuss the dynamical behavior of the governing (1+1)-dimensional time–space Salerno equation, which describes the discrete electrical lattice with nonlinear dispersion. The different kinds of solutions in the form of periodic, Jacobi elliptic, and exponential functions are obtained by the two analytical approaches, namely the modified generalized exponential rational function method (MGERFM) and the extended sinh-Gordon equation expansion method (shGEEM). The MGERF approach is applied to construct exact solitary wave solutions containing trigonometry, hyperbolic and exponential functions, while the extended shGEE technique is employed to obtain periodic wave solutions containing hyperbolic and Jacobi elliptic functions via performing the symbolic computation in the software package MATHEMATICA. Moreover, by means of standard linear-stability analysis, the modulation instability (MI) and the MI gain spectrum is analytically computed for the considered equation. By selecting suitable parametric values, solution profiles are portrayed in order to make the solutions physically relevant. These results yield periodic waves, kink waves, multi-soliton, and their interactions. By comparing the obtained solutions to the previous findings, we can reveal the novelty of the solutions. In addition, all the obtained solutions were verified by substituting them back into the governing equation using the Mathematica software. The acquired results are significant for the study of wave propagation, signal transmission, and applications of super-transmission phenomena.

Suggested Citation

  • Mann, Nikita & Rani, Setu & Kumar, Sachin & Kumar, Raj, 2024. "Novel closed-form analytical solutions and modulation instability spectrum induced by the Salerno equation describing nonlinear discrete electrical lattice via symbolic computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 473-490.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:473-490
    DOI: 10.1016/j.matcom.2023.12.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423005384
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.12.031?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Rizvi, Syed Tahir Raza & Khan, Salah Ud-Din & Hassan, Mohsan & Fatima, Ishrat & Khan, Shahab Ud-Din, 2021. "Stable propagation of optical solitons for nonlinear Schrödinger equation with dispersion and self phase modulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 126-136.
    2. Ali, Karmina K. & Yokus, Asıf & Seadawy, Aly R. & Yilmazer, Resat, 2022. "The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Zhou, Qin & Triki, Houria & Xu, Jiakun & Zeng, Zhongliang & Liu, Wenjun & Biswas, Anjan, 2022. "Perturbation of chirped localized waves in a dual-power law nonlinear medium," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Yun-Mei Zhao, 2013. "F -Expansion Method and Its Application for Finding New Exact Solutions to the Kudryashov-Sinelshchikov Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, April.
    5. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz & Bashir, Azhar, 2022. "Lump solutions, Kuznetsov–Ma breathers, rogue waves and interaction solutions for magneto electro-elastic circular rod," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    Full references (including those not matched with items on IDEAS)

    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. Triki, Houria & Sun, Yunzhou & Zhou, Qin & Biswas, Anjan & Yıldırım, Yakup & Alshehri, Hashim M., 2022. "Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Aly R. Seadawy & Hanadi Zahed & Mujahid Iqbal, 2022. "Solitary Wave Solutions for the Higher Dimensional Jimo-Miwa Dynamical Equation via New Mathematical Techniques," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    3. Ali, Karmina K. & Faridi, Waqas Ali & Tarla, Sibel, 2024. "Phase trajectories and Chaos theory for dynamical demonstration and explicit propagating wave formation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Soltani, Mourad & Triki, Houria & Azzouzi, Faiçal & Sun, Yunzhou & Biswas, Anjan & Yıldırım, Yakup & Alshehri, Hashim M. & Zhou, Qin, 2023. "Pure–quartic optical solitons and modulational instability analysis with cubic–quintic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Chen, Yi-Xiang, 2023. "Vector peregrine composites on the periodic background in spin–orbit coupled Spin-1 Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Cheng, Li & Zhang, Yi & Ma, Wen-Xiu & Ge, Jian-Ya, 2021. "Wronskian and lump wave solutions to an extended second KP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 720-731.
    7. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. Cao, Qi-Hao & Geng, Kai-Li & Zhu, Bo-Wei & Wang, Yue-Yue & Dai, Chao-Qing, 2023. "Scalar vortex solitons and vector dipole solitons in whispering gallery mode optical microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    9. Ismael, Hajar Farhan & Sulaiman, Tukur Abdulkadir, 2023. "On the dynamics of the nonautonomous multi-soliton, multi-lump waves and their collision phenomena to a (3+1)-dimensional nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    10. Yang, Liu & Gao, Ben, 2024. "The nondegenerate solitons solutions for the generalized coupled higher-order nonlinear Schrödinger equations with variable coefficients via the Hirota bilinear method," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    11. 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).
    12. Zeng, Liangwei & Belić, Milivoj R. & Mihalache, Dumitru & Zhu, Xing, 2024. "Elliptical and rectangular solitons in media with competing cubic–quintic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    13. Chen, Liang-Yuan & Wu, Hong-Yu & Jiang, Li-Hong, 2024. "Ring-like two-breather structures of a partially nonlocal NLS system with different two-directional diffractions under a parabolic potential," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    14. Rafiq, Muhammad Naveed & Chen, Haibo, 2024. "Dynamics of three-wave solitons and other localized wave solutions to a new generalized (3+1)-dimensional P-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

    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:219:y:2024:i:c:p:473-490. 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.