Abstract
In this work, the (2+1)-dimensional chiral nonlinear Schrödinger equation that describes about quantum field concept in physics and other physical sciences are studied and solved by utilizing the two modern techniques including the polynomial expansion method and the Sardar sub-equation method. We attained different types of soliton solutions that had been applications in different fields of mathematical sciences. The behaviours of attained solutions are periodic, singular and v-shaped soliton solutions. Furthermore, we have investigated the stability of the obtained results. Also, the 3D, 2D, and contour graphics are displayed for the better understanding of the dynamical behaviour of various waves structures extensively. The techniques applied in this article are not used in this model in literature so we say that our findings are new that summarize the novelty of work. The utilize model has applications in physics related phenomenon also obtained results highly valuable in various branches of sciences specially in the transmission of fiber optical.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs11082-024-06920-8/MediaObjects/11082_2024_6920_Fig7_HTML.png)
Similar content being viewed by others
Availability of data and materials
Data sharing not applicable to this article as no data sets were generated or analyzed during this study.
References
Abdelwahed, H., Alsarhan, A., El-Shewy, E., Abdelrahman, M.A., et al.: Novel explosive and super fractional nonlinear schrödinger structures. J. Math. (2023)
Abdelwahed, H., Alsarhana, A., El-Shewy, E., Abdelrahman, M.A.: Characteristics of new stochastic solitonic solutions for the chiral type of nonlinear schrödinger equation. Fractal Fractional 7(6), 461 (2023)
Ahmad, S., Saifullah, S., Khan, A., Inc, M.: New local and nonlocal soliton solutions of a nonlocal reverse space-time mkdv equation using improved hirota bilinear method. Phys. Lett. A 450, 128393 (2022)
Ahmad, J., Mustafa, Z., Turki, N.B., Shah, N.A., et al.: Solitary wave structures for the stochastic nizhnik-novikov-veselov system via modified generalized rational exponential function method. Res. Phys. 52, 106776 (2023)
Ahmad, J., Noor, K., Anwar, S., Akram, S.: Stability analysis and soliton solutions of truncated m-fractional heisenberg ferromagnetic spin chain model via two analytical methods. Opt. Quant. Electronics 56(1), 95 (2024)
Akinyemi, L., Inc, M., Khater, M.M., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electronics 54(3), 191 (2022)
Akram, S., Ahmad, J., Alkarni, S., Shah, N.A., et al.: Analysis of lump solutions and modulation instability to fractional complex ginzburg-landau equation arise in optical fibers. Res. Phys. 53, 106991 (2023)
Akram, S., Ahmad, J., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modelled by perturbed nonlinear schrödinger equation and stability analysis. Opt. Quant. Electronics 55(5), 450 (2023)
Almatrafi, M., Alharbi, A.: New soliton wave solutions to a nonlinear equation arising in plasma physics., CMES Comput. Model. Eng. Sci. 137(1)
Almuneef, A., Alqahtani, Z., El-Shewy, E., Abdelrahman, M.A.: Simulation of new waves in applied sciences via schrödinger equations. J. Taibah Univ. Sci. 18(1), 2285082 (2024)
Arnous, A.H., Hashemi, M.S., Nisar, K.S., Shakeel, M., Ahmad, J., Ahmad, I., Jan, R., Ali, A., Kapoor, M., Shah, N.A.: Investigating solitary wave solutions with enhanced algebraic method for new extended sakovich equations in fluid dynamics. Res. Phys. 57, 107369 (2024)
Arora, G., Rani, R., Emadifar, H.: Numerical solutions of nonlinear schrodinger equation with applications in optical fiber communication. Optik 266, 169661 (2022)
Arshad, M., Seadawy, A.R., Lu, D.: Bright-dark solitary wave solutions of generalized higher-order nonlinear schrödinger equation and its applications in optics. J. Electromagnetic Waves Appl. 31(16), 1711–1721 (2017)
Arshad, M., Seadawy, A.R., Lu, D.: Study of soliton solutions of higher-order nonlinear schrödinger dynamical model with derivative non-kerr nonlinear terms and modulation instability analysis. Res. Phys. 13, 102305 (2019)
Belyaev, A., Dunster, J.L., Gibbins, J.M., Panteleev, M.A., Volpert, V.: Modeling thrombosis in silico: frontiers, challenges, unresolved problems and milestones. Phys. Life Rev. 26, 57–95 (2018)
El-Rashidy, K.: New traveling wave solutions for the higher Sharma–Tasso–Olver equation by using extension exponential rational function method. Res. Phys. 17, 103066 (2020)
Hosseini, K., Mirzazadeh, M., Osman, M., Al Qurashi, M., Baleanu, D.: Solitons and jacobi elliptic function solutions to the complex Ginzburg–Landau equation. Front. Phys. 8, 225 (2020)
Huang, W.-H.: A polynomial expansion method and its application in the coupled Zakharov–Kuznetsov equations. Chaos Solitons Fractals 29(2), 365–371 (2006)
Islam, N., Khan, K., Islam, M.H.: Travelling wave solution of Dodd–Bullough–Mikhailov equation: a comparative study between generalized kudryashov and improved f-expansion methods. J. Phys. Commun. 3(5), 055004 (2019)
Islam, M.T., Akbar, M.A., Ahmad, H., Ilhan, O.A., Gepreel, K.A.: Diverse and novel soliton structures of coupled nonlinear schrödinger type equations through two competent techniques. Mod. Phys. Lett. B 36(11), 2250004 (2022)
Islam, M.T., Sarkar, T.R., Abdullah, F.A., Gómez-Aguilar, J.: Distinct optical soliton solutions to the fractional hirota maccari system through two separate strategies. Optik 300, 171656 (2024)
Javeed, S., Abbasi, M.A., Imran, T., Fayyaz, R., Ahmad, H., Botmart, T.: New soliton solutions of simplified modified camassa holm equation, Klein–Gordon–Zakharov equation using first integral method and exponential function method. Res. Phys. 38, 105506 (2022)
Karjanto, N.: The nonlinear schrödinger equation: A mathematical model with its wide-ranging applications, ar**v preprint ar**v:1912.10683
Khater, M., Anwar, S., Tariq, K.U., Mohamed, M.S.: Some optical soliton solutions to the perturbed nonlinear schrödinger equation by modified khater method. AIP Adv. 11(2)
Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H., Eslami, M.: Sine-gordon expansion method for exact solutions to conformable time fractional equations in rlw-class. J. King Saud Univ. Sci. 32(1), 567–574 (2020)
Mohammed, W.W., Albalahi, A., Albadrani, S., Aly, E., Sidaoui, R., Matouk, A.: The analytical solutions of the stochastic fractional kuramoto-sivashinsky equation by using the Riccati equation method. Math. Prob. Eng. 2022, 1–8 (2022)
Peng, X., Zhao, Y.-W., Lü, X.: Data-driven solitons and parameter discovery to the (2+ 1)-dimensional nlse in optical fiber communications. Nonlinear Dyn., pp. 1–16 (2023)
Rehman, S.-U., Bilal, M., Ahmad, J.: Highly dispersive optical and other soliton solutions to fiber bragg gratings with the application of different mechanisms. Int. J. Mod. Phys. B 36(28), 2250193 (2022)
Rehman, H.U., Akber, R., Wazwaz, A.-M., Alshehri, H.M., Osman, M.: Analysis of Brownian motion in stochastic Schrödinger wave equation using sardar sub-equation method. Optik 289, 171305 (2023)
Tariq, K.U., Wazwaz, A., Kazmi, S.R.: On the dynamics of the (2+ 1)-dimensional chiral nonlinear Schrödinger model in physics. Optik 285, 170943 (2023)
Ur Rehman, S., Ahmad, J.: Stability analysis and novel optical pulses to Kundu–Mukherjee–Naskar model in birefringent fibers. Int. J. Mod. Phys. B 2450192 (2023)
Ur Rehman, H., Asjad Imran, M., Bibi, M., Riaz, M., Akgül, A.: New soliton solutions of the 2d-chiral nonlinear Schrodinger equation using two integration schemes. Math. Methods Appl. Sci. 44(7), 5663–5682 (2021)
Wang, J., Krstic, M.: Delay-compensated event-triggered boundary control of hyperbolic pdes for deep-sea construction. Automatica 138, 110137 (2022)
Yang, X.-J., Kumar, D., et al.: New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics. Frontiers Media SA, Lausanne (2023)
Younas, U., Sulaiman, T.A., Ren, J.: On the study of optical soliton solutions to the three-component coupled nonlinear schrödinger equation: applications in fiber optics. Opt. Quant. Electronics 55(1), 72 (2023)
Zafar, A., Ali, K.K., Raheel, M., Nisar, K.S., Bekir, A.: Abundant m-fractional optical solitons to the pertubed Gerdjikov–Ivanov equation treating the mathematical nonlinear optics. Opt. Quant. Electronics 54(1), 25 (2022)
Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E., Yıldırım, Y.: Optical solitons for the perturbed Biswas–Milovic equation with Kudryashov’s law of refractive index by the unified auxiliary equation method. Optik 230, 166286 (2021)
Funding
Not available.
Author information
Authors and Affiliations
Contributions
XZ and KUT supervised the project, handled administration, developed methodology, conceptualized, and validated. HR was responsible for identifying the research problem, analyzing outcomes, and reviewing and editing. SMRK conducted formal analysis and investigation, wrote the original draft. MAH handled visualization, analyzed the outcomes, and participated in the review and editing process.
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no Conflict of interest.
Ethics approval
Not applicable.
Consent for publication
All the authors have agreed and given their consent for the publication of this research paper.
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.
About this article
Cite this article
Zhou, X., Tariq, K.U., Rezazadeh, H. et al. Stability and solitonic wave solutions of (2+1)-dimensional chiral nonlinear Schrödinger equation. Opt Quant Electron 56, 1228 (2024). https://doi.org/10.1007/s11082-024-06920-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-024-06920-8