Skip to main content
SpringerLink
Log in

Pulse-driven robot: motion via distinct lumps and rogue waves

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

Waves advantageous properties have recently been exploited to enable a wide range of applications, including impact reduction, switching, focussing, and asymmetric transmission. We find that the motion of lumps, rogue waves, lump periodic waves, Ma-breather waves, lump one-strip, and generalised breather waves may also be used to build flexible constructions crawl. Symbolic computation and the Hirota bilinear method are used to create these nonlinear waves. Combining the aforementioned approaches, we demonstrate that such pulse-driven locomotion achieves optimal effectiveness when the pulses are solitons. Our research shows how nonlinear waves can be used in a variety of new ways, including as a platform for developing adaptable robots that can move.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availibility

Not applicable.

References

  • Ahmad, A., Seadawy, A.R., Ahmed, S., Rizvi, S.T.: Dynamical forms of breathers, rogue waves, lump and their interactions for Schrödinger-Hirota equation. Optic. Quantum Electr. 55(8), 730 (2023)

    Google Scholar 

  • Ahmed, S., Ashraf, R., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, A., El-Shehawi, A.M.: Lump, multi-wave, kinky breathers, interactional solutions and stability analysis for general \((2+ 1)\)-rth dispersionless Dym equation. Res. Phys. 25, 104160 (2021)

    Google Scholar 

  • Ahmed, S., Seadawy, A.R., Rizvi, S.T., Ahmad, A.: Study of dissipative NLSE for dark and bright, multiwave, breather and M-shaped solitons along with some interactions in monochromatic waves. Optic. Quantum Electr. 54(12), 782 (2022)

    Google Scholar 

  • Ahmed, S., Seadawy, A.R., Rizvi, S.T.: Study of breathers, rogue waves and lump solutions for the nonlinear chains of atoms. Optic. Quantum Electr. 54(5), 1–28 (2022)

    Google Scholar 

  • Ahmed, S., Seadawy, A.R., Rizvi, S.T., Mubaraki, A.M.: Homoclinic breathers and soliton propagations for the nonlinear (3+ 1)-dimensional Geng dynamical equation. Res. Phys. 52, 106822 (2023)

    Google Scholar 

  • Ahmed, S., Seadawy, A.R., Rizvi, S.T., Raza, U.: Multi-Peak and Propagation Behavior of M-Shape Solitons in (2+ 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem. Fract. Fract. 7(10), 709 (2023)

    Google Scholar 

  • Ahmed, S., Seadawy, A. R., Rizvi, S. T.,  Hameed, M.: Multi-peak and rational soliton propagations for (3+ 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup Kupershmidt model in fluid mechanics, ocean dynamics and plasma physics. Int. J. Geometr. Methods Mod. Phys., 2350158 (2023)

    Article  Google Scholar 

  • Akram, U., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, S., Sayed, S.: Traveling wave solutions for the fractional Wazwaz-Benjamin-Bona-Mahony model in arising shallow water waves. Res. Phys. 20, 103725 (2021)

    Google Scholar 

  • Ali, K., Seadawy, A.R., Ahmed, S., Rizvi, S.T.: Discussion on rational solutions for Nematicons in liquid crystals with Kerr Law. Chaos Solit. Fract. 160, 112218 (2022)

    MathSciNet  Google Scholar 

  • Bertoldi, K., Vitelli, V., Christensen, J., Van Hecke, M.: Flexible mechanical metamaterials. Nat. Rev. Mater. 2(11), 1–11 (2017)

    Google Scholar 

  • Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., El-Rashidy, K., Mahmoud, S.F.: Analytical wave structures in plasma physics modelled by Gilson-Pickering equation by two integration norms. Res. Phys. 23, 103959 (2021)

    Google Scholar 

  • Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Zahed, H.: Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin-Gottwald-Holm system and modulation instability analysis. Math. Methods Appl. Sci. 44(5), 4094–4104 (2021)

    MathSciNet  ADS  Google Scholar 

  • Deng, B., Raney, J.R., Tournat, V., Bertoldi, K.: Elastic vector solitons in soft architected materials. Phys. Rev. Lett. 118(20), 204102 (2017)

    CAS  PubMed  ADS  Google Scholar 

  • Deng, B., Wang, P., He, Q., Tournat, V., Bertoldi, K.: Metamaterials with amplitude gaps for elastic solitons. Nat. Commun. 9(1), 3410 (2018)

    PubMed  PubMed Central  ADS  Google Scholar 

  • Deng, B., Chen, L., Wei, D., Tournat, V., Bertoldi, K.: Pulse-driven robot: motion via solitary waves. Sci. Adv. 6(18), 1166 (2020)

    PubMed  PubMed Central  ADS  Google Scholar 

  • Edelman, M.: Comments on a note on stability of fractional logistic maps. Appl. Math. Lett. 125, 107787 (2022)

    MathSciNet  Google Scholar 

  • Ghaffar, A., Ali, A., Ahmed, S., Akram, S., Baleanu, D., Nisar, K.S.: A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order. Adv. Diff. Equ. 1, 1–15 (2020)

    MathSciNet  Google Scholar 

  • Hietarinta, J. Introduction to the Hirota bilinear method: Integrability of Nonlinear Systems, Springer, Berlin, Heidelberg, 95–103 (1997)

  • Holmes, D.P.: Elasticity and stability of shape-shifting structures. Curr. Opin. Colloid Interf. Sci. 40, 118–137 (2019)

    CAS  Google Scholar 

  • Jin-Ming, Z., Yao-Ming, Z.: The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq-Burgers equation. Chinese Phys. B. 20(1), 010205 (2011)

    Google Scholar 

  • Li, X.L., Guo, R.: Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan-Porsezian-Daniel Equations in Birefringent Optical Fibers. Annalen der Physik 535(1), 2200472 (2023)

    ADS  Google Scholar 

  • Liu, Y., Wen, X.Y., Wang, D.S.: The N-soliton solution and localized wave interaction solutions of the \((2+ 1)\)-dimensional generalized Hirota-Satsuma equation. Comput. Math. Appl. 77(4), 947–966 (2019)

    MathSciNet  Google Scholar 

  • Liu, Y., Li, B., Wazwaz, A.M.: Novel high-order breathers and rogue waves in the Boussinesq equation via determinants. Int. J. Mod. Phys. B 43(6), 3701–3715 (2020)

    MathSciNet  Google Scholar 

  • Ma, Y.L.: N-solitons, breathers and rogue waves for a generalized Boussinesq equation. Int. J. Comput. Math. 97(8), 1648–1661 (2020)

    MathSciNet  Google Scholar 

  • Osman, M.S.: Multi-soliton rational solutions for some nonlinear evolution equations. Open Phys. 14(1), 26–36 (2016)

    ADS  Google Scholar 

  • Raney, J.R., Nadkarni, N., Daraio, C., Kochmann, D.M., Lewis, J.A., Bertoldi, K.: Stable propagation of mechanical signals in soft media using stored elastic energy. Proc. Natl. Acad. Sci. 113(35), 9722–9727 (2016)

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  • Rizvi, S. T. R., Ahmed, S.: Resonant collisions among X-type, multi-lump, generalized breathers, N-solitons and rogue waves in plasma, Optik, 171390 (2023)

  • Rizvi, S. T., Seadawy, A. R., Ahmed, S., & Ashraf, R.: Lax pair, Darboux transformation, Weierstrass-Jacobi elliptic and generalized breathers along with soliton solutions for Benjamin-Bona-Mahony equation. Int. J. Mod. Phys. B, 2350233 (2023)

  • Rizvi, S. T., Seadawy, A. R., Farah, N., Ahmed, S.: Transformation and interactions among solitons in metamaterials with quadratic-cubic nonlinearity and inter-model dispersion. Int. J. Mod. Phys. B, 2350087 (2022)

  • Rizvi, S.T.R., Seadawy, A.R., Younis, M., Ali, I., Althobaiti, S., Mahmoud, S.F.: Soliton solutions, Painleve analysis and conservation laws for a nonlinear evolution equation. Res. Phys. 23, 103999 (2021a)

    Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Younis, M., Iqbal, S., Althobaiti, S., El-Shehawi, A.M.: Various optical soliton for a weak fractional nonlinear Schrödinger equation with parabolic law. Res. Phys. 23, 103998 (2021b)

    Google Scholar 

  • Rizvi, S.T., Seadawy, A.R., Ahmed, S., Ali, K.: Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions. Optic. Quantum Electr. 55(2), 1–25 (2023)

    Google Scholar 

  • Rizvi, S. T., Seadawy, A. R., Ahmed, S.,  Ashraf, F.: Novel rational solitons and generalized breathers for (1+ 1)-dimensional longitudinal wave equation. Int. J. Mod. Phys. B, 2350269 (2023)

    Article  Google Scholar 

  • Seadawy, A.R., Bilal, M., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique. Chaos Solit. Fract. 144, 110669 (2021a)

    MathSciNet  Google Scholar 

  • Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation. Phys. Script. 96(4), 045202 (2021b)

    CAS  ADS  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter-Saxton equation. Open Phys. 19(1), 1–10 (2021)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ali, I., Younis, M., Ali, K., Makhlouf, M.M., Althobaiti, A.: Conservation laws, optical molecules, modulation instability and Painlevé analysis for the Chen-Lee-Liu model. Optic. Quantum Electr. 53(4), 1–15 (2021)

    Google Scholar 

  • Seadawy, A.R., Rehman, S.U., Younis, M., Rizvi, S.T.R., Althobaiti, S., Makhlouf, M.M.: Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation. Phys. Scrip. 96(4), 045202 (2021)

    CAS  ADS  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation. Chaos Solit. Frac. 160, 112258 (2022a)

    Google Scholar 

  • Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics. J. Geomet. Phys. 176, 104507 (2022b)

    MathSciNet  Google Scholar 

  • Seadawy, A.R., Ahmed, S., Rizvi, S.T., Ali, K.: Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system. Chaos Solit. Fract. 161, 112307 (2022c)

    MathSciNet  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized Fitzhugh-Nagumo equation: Applications in nuclear reactor theory. Chaos Solitons Fract. 161, 112326 (2022d)

    MathSciNet  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Solitons collision and multi-peak solutions for a new (3+ 1)-dimensional NLSE describing pulse propagation in optical fibers. Optic. Quantum Electr. 55(5), 467 (2023)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S.: Analytical solutions along with grey-black optical solitons under the influence of self-steepening effect and third order dispersion. Optic. Quantum Electr. 55(3), 288 (2023)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S., Batool, T.: Propagation of W-shaped and M-shaped solitons with multi-peak interaction for ultrashort light pulse in fibers. Optic. Quantum Electr. 55(3), 1–23 (2023a)

    Google Scholar 

  • Seadawy, A.R., Ahmed, S., Rizvi, S.T., Nazar, K.: Applications for mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation in water wave flumes and optical fibers. Optic. Quantum Electr. 55(1), 34 (2023b)

    Google Scholar 

  • Seaway, A. R., Rizvi, S. T., Ahmad, A., Ahmed, S.: Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis-Procesi equation. Int. J. Mod. Phys. B, (2023) 2350172

  • Shen, S., Yang, Z., Li, X., Zhang, S.: Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media. Commun. Nonlinear Sci. Num. Simul. 103, 106005 (2021)

    MathSciNet  Google Scholar 

  • Shen, S., Yang, Z.J., Pang, Z.G., Ge, Y.R.: The complex-valued astigmatic cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. Appl. Math. Lett. 125, 107755 (2022)

    Google Scholar 

  • Song, L.M., Yang, Z.J., Li, X.L., Zhang, S.M.: Coherent superposition propagation of Laguerre-Gaussian and Hermite-Gaussian solitons. Appl. Math. Lett. 102, 106114 (2020)

    MathSciNet  Google Scholar 

  • Tariq, K.U., Zainab, H., Seadawy, A.R., Younis, M., Rizvi, S.T.R., Abd Allah, A.M.: On some novel optical wave solutions to the paraxial M-fractional nonlinear Schrödinger dynamical equation. Optic. Quant. Electr. 53(5), 1–14 (2021)

    Google Scholar 

  • Yi, H., Yao, Y., Zhang, X., & Ma, G.: High-order effect on the transmission of two optical solitons. Chinese Physics B, 32(10), 100509 (2023)

  • Younas, U., Younis, M., Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S., Sayed, S.: Diverse exact solutions for modified nonlinear Schrödinger equation with conformable fractional derivative. Res. Phys. 20, 103766 (2021)

    Google Scholar 

  • Younis, M., Seadawy, A. R., Bilal, M., Rizvi, S. T. R., Althobaiti, S., Alkafafy, M.: Nonlinear dynamical wave structures to the Date-Jimbo-Kashiwara-Miwa equation and its modulation instability analysis. Mod. Phys. Lett. B, 2150300 (2021a)

  • Younis, M., Younas, U., Bilal, M., Rehman, S. U., Rizvi, S. T. R.: Investigation of optical solitons with Chen-Lee-Liu equation of monomode fibers by five free parameters. Indian J. Phys. 1–8 (2021b)

Download references

Acknowledgements

The researchers would like to acknowledge Deanship of Scientific Research, Taif University for assistance this work.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

    Sarfaraz Ahmed

  2. Department of Mathematics and Statistics, Collage of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia

    Ali M. Mubaraki

Authors
  1. Sarfaraz Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ali M. Mubaraki
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

SA: visualization, investigation, conceptualization, methodology, writing original draft. AMM: software, validation, data curation, writing review and editing

Corresponding author

Correspondence to Sarfaraz Ahmed.

Ethics declarations

Conflict of interest

The authors state that they do not have any conflict of interest.

Ethical approval

I hereby declare that this manuscript is the result of my independent creation under the reviewer’s comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmed, S., Mubaraki, A.M. Pulse-driven robot: motion via distinct lumps and rogue waves. Opt Quant Electron 56, 225 (2024). https://doi.org/10.1007/s11082-023-05816-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05816-3

Keywords

Search

Navigation