IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922010864.html
   My bibliography  Save this article

A family of nonlinear Schrodinger equations and their solitons solutions

Author

Listed:
  • El-Nabulsi, Rami Ahmad
  • Anukool, Waranont

Abstract

In this communication, three different forms of fractional nonlinear Schrödinger equations have been constructed based on the notion of nonlocal generalized fractional momentum operator, the fractional expansion Riccati method and the notion of Laplacian operator in fractal dimensions. Their physical properties are analyzed and their associated solitonic solutions are obtained and discussed. It was observed that the first two approaches give comparable solutions, whereas the third approach give rise to a nonlinear Schrödinger equation characterized by variable coefficients, and hence, a large family of solitons solutions may be obtained accordingly.

Suggested Citation

  • El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2023. "A family of nonlinear Schrodinger equations and their solitons solutions," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010864
    DOI: 10.1016/j.chaos.2022.112907
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922010864
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112907?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. Sara H. M. Hamed & Eltayeb A. Yousif & Arbab I. Arbab, 2014. "Analytic and Approximate Solutions of the Space-Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, October.
    2. Chenkuan Li & Changpin Li & Thomas Humphries & Hunter Plowman, 2019. "Remarks on the Generalized Fractional Laplacian Operator," Mathematics, MDPI, vol. 7(4), pages 1-17, March.
    3. Jason W. Fleischer & Mordechai Segev & Nikolaos K. Efremidis & Demetrios N. Christodoulides, 2003. "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature, Nature, vol. 422(6928), pages 147-150, March.
    4. Kudryashov, Nikolay A., 2020. "Highly dispersive optical solitons of equation with various polynomial nonlinearity law," Chaos, Solitons & Fractals, Elsevier, vol. 140(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. Dong, Hoang Minh & Hien, Nguyen Thi Thu & Bang, Nguyen Huy & Van Doai, Le, 2024. "Dynamics of twin pulse propagation and dual-optical switching in a Λ + Ξ atomic medium," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Qi, Linming & Liu, Lu & Zhao, Weiliang, 2024. "Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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. Kumar, Vikas & Biswas, Anjan & Ekici, Mehmet & Moraru, Luminita & Alzahrani, Abdullah Khamis & Belic, Milivoj R., 2021. "Time–dependent coupled complex short pulse equation: Invariant analysis and complexitons," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Rami Ahmad El-Nabulsi & Waranont Anukool, 2023. "A generalized nonlinear cubic-quartic Schrodinger equation and its implications in quantum wire," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(5), pages 1-8, May.
    3. Sucu, Nuray & Ekici, Mehmet & Biswas, Anjan, 2021. "Stationary optical solitons with nonlinear chromatic dispersion and generalized temporal evolution by extended trial function approach," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Bao, Y.Y. & Li, S.R. & Liu, Y.H. & Xu, T.F., 2022. "Gap solitons and nonlinear Bloch waves in fractional quantum coupler with periodic potential," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Pawel S. Jung & Georgios G. Pyrialakos & Fan O. Wu & Midya Parto & Mercedeh Khajavikhan & Wieslaw Krolikowski & Demetrios N. Christodoulides, 2022. "Thermal control of the topological edge flow in nonlinear photonic lattices," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    6. Panajotov, Krassimir & Tlidi, Mustapha & Song, Yufeng & Zhang, Han, 2022. "Discrete vector light bullets in coupled χ3 nonlinear cavities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Kartashov, Yaroslav V., 2023. "Vortex solitons in large-scale waveguide arrays with adjustable discrete rotational symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Islam Samir & Ahmed H. Arnous & Yakup Yıldırım & Anjan Biswas & Luminita Moraru & Simona Moldovanu, 2022. "Optical Solitons with Cubic-Quintic-Septic-Nonic Nonlinearities and Quadrupled Power-Law Nonlinearity: An Observation," Mathematics, MDPI, vol. 10(21), pages 1-9, November.
    9. Peng Wang & Qidong Fu & Ruihan Peng & Yaroslav V. Kartashov & Lluis Torner & Vladimir V. Konotop & Fangwei Ye, 2022. "Two-dimensional Thouless pumping of light in photonic moiré lattices," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    10. Li, S.R. & Bao, Y.Y. & Liu, Y.H. & Xu, T.F., 2022. "Bright solitons in fractional coupler with spatially periodical modulated nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Oswaldo González-Gaxiola & Anjan Biswas & Yakup Yıldırım & Luminita Moraru, 2022. "Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition," Mathematics, MDPI, vol. 10(9), pages 1-12, May.
    12. Anjan Biswas & Jose Vega-Guzman & Yakup Yıldırım & Luminita Moraru & Catalina Iticescu & Abdulah A. Alghamdi, 2023. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    13. Feng, Bao-Feng & Chan, Youn-Sha, 2007. "Intrinsic localized modes in a three particle Fermi–Pasta–Ulam lattice with on-site harmonic potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 292-301.
    14. Shi, Zeyun & Badshah, Fazal & Qin, Lu, 2023. "Two-dimensional lattice soliton and pattern formation in a cold Rydberg atomic gas with nonlocal self-defocusing Kerr nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    15. Nigus Demelash Melaku & Ali Fares & Ripendra Awal, 2023. "Exploring the Impact of Winter Storm Uri on Power Outage, Air Quality, and Water Systems in Texas, USA," Sustainability, MDPI, vol. 15(5), pages 1-19, February.
    16. Nikolay A. Kudryashov, 2022. "Optical Solitons of the Generalized Nonlinear Schrödinger Equation with Kerr Nonlinearity and Dispersion of Unrestricted Order," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    17. Chen, Guanwei & Ma, Shiwang, 2014. "Homoclinic solutions of discrete nonlinear Schrödinger equations with asymptotically or super linear terms," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 787-798.
    18. Li, Chunyan & Konotop, Vladimir V. & Malomed, Boris A. & Kartashov, Yaroslav V., 2023. "Bound states in Bose-Einstein condensates with radially-periodic spin-orbit coupling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    19. Cabanas, A.M. & Vélez, J.A. & Pérez, L.M. & Díaz, P. & Clerc, M.G. & Laroze, D. & Malomed, B.A., 2021. "Dissipative structures in a parametrically driven dissipative lattice: Chimera, localized disorder, continuous-wave, and staggered states," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    20. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Peng, Jianle & He, Yingji, 2018. "Generation of multivortex ring beams by inhomogeneous effective diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 30-36.

    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:chsofr:v:166:y:2023:i:c:s0960077922010864. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.