Abstract
In this work, we study the exact traveling wave solutions of \((2+1)\)-dimensional Chiral nonlinear Schrödinger equation with the aid of generalized auxiliary equation method. The aforementioned model is used as a governing equation to discuss the wave in quantum field theory. The suggested technique is direct, effective, powerful, and offers constraint conditions to ensure the existence of solutions. The solutions obtained are bright solitons, dark solitons, singular solitons, mixed solitons, periodic waves, exponential, rational, and complex solutions that are relevant in various applications of applied science. Finally, some solutions are depicted in two and three dimensional to better understand the behavior of the considered model.
Similar content being viewed by others
References
Abdou, M.A.: A generalized auxiliary equation method and its applications. Nonlinear Dyn. 52(1), 95–102 (2008)
Ablowitz, M.J.: Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons. Cambridge University Press, Cambridge (2011)
Ablowitz, M.J., Prinari, B., Trubatch, A.D.: Discrete and Continuous Nonlinear Schrödinger Systems. Cambridge University Press, Cambridge (2004)
Akinyemi, L., Iyiola, O.S.: Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Math. Methods Appl. Sci. 43(12), 7442–7464 (2020). https://doi.org/10.1002/mma.6484
Akinyemi, L., Senol, M., Huseen, S.N.: Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma. Adv. Differ. Eqn. 2021(1), 1–27 (2021a). https://doi.org/10.1186/s13662-020-03208-5
Akinyemi, L., Senol, M., Iyiola, O.S.: Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method. Math. Comput. Simul. 182, 211–233 (2021b). https://doi.org/10.1016/j.matcom.2020.10.017
Alagesan, T., Uthayakumar, A., Porsezian, K.: Painlev analysis and Backlund transformation for a three-dimensional Kadomtsev–Petviashvili equation. Chaos Solitons Fract. 8, 893–895 (1997)
Ali Akbar, M., Akinyemi, L., Yao, S.-W., Jhangeer, A., Rezazadeh, H., Khater, M.M.A., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results Phys. 25, 1–10 (2021). https://doi.org/10.1016/j.rinp.2021.104228
Az-Zo’bi, E.A., AlZoubi, W.A., Akinyemi, L., et al.: Abundant closed-form solitons for time-fractional integro-differential equation in fluid dynamics. Opt. Quant. Electron. 53, 1–16 (2021). https://doi.org/10.1007/s11082-021-02782-6
Bekir, A., Guner, O., Ünsal, Ö., Mirzazadeh, M.: Applications of fractional complex transform and \((G^{\prime }/G)\)-expansion method for time-fractional differential equations. J. Appl. Anal. Comput. 6(1), 131–144 (2016)
Biswas, A., Jawad, A.J.M., Manrakhan, W.N., Sarma, A.K., Khan, K.R.: Optical solitons and complexitons of the Schrödinger–Hirota equation. Opt. Laser Technol. 44(7), 2265–2269 (2012)
Bulut, H., Sulaiman, T.A., Demirdag, B.: Dynamics of soliton solutions in the chiral nonlinear Schrödinger equations. Nonlinear Dyn. 91, 1985–1991 (2018). https://doi.org/10.1007/s11071-017-3997-9
Eslami, M.: Trial solution technique to chiral nonlinear Schrödinger’s equation in \((1+2)\)-dimensions. Nonlinear Dyn. 85(2), 813–816 (2016)
Fan, E.G., Zhang, Q.H.: A note on the homogeneous balance method. Phys. Lett. A 246, 403–406 (1998)
Gao, W., Veeresha, P., Prakasha, D.G., Baskonus, H.M.: New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques. Numer. Methods Partial Differ. Eqn. 37(1), 210–243 (2021)
Ghanbari, B., Inc, M., Rada, L.: Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach. J. Appl. Anal. Comput. 9(2), 568–589 (2019)
He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fract. 30(3), 700–708 (2006)
Hosseini, K., Ansari, R.: New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method. Waves Random Complex Media 27(4), 628–636 (2017). https://doi.org/10.1080/17455030.2017.1296983
Hosseini, K., Mirzazadeh, M.: Soliton and other solutions to the \((1+2)\)-dimensional chiral nonlinear Schrödinger equation. Commun. Theor. Phys. 72(12), 1–6 (2020)
Houwe, A., Yakada, S., Abbagari, S., Saliou, Y., Inc, M., Doka, S.Y.: Survey of third-and fourth-order dispersions including ellipticity angle in birefringent fibers on W-shaped soliton solutions and modulation instability analysis. Eur. Phys. J. Plus 136(4), 1–27 (2021)
Khater, M.M., Inc, M., Attia, R.A., Lu, D., Almohsen, B.: Abundant new computational wave solutions of the GM-DP-CH equation via two modified recent computational schemes. J. Taibah Univ. Sci. 14(1), 1554–1562 (2020)
Korkmaz, A., Hosseini, K.: Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Opt. Quant. Electron. 49(8), 1–10 (2017). https://doi.org/10.1007/s11082-017-1116-2
Korpinar, Z., Tchier, F., Inc, M., Bousbahi, F., Tawfiq, F.M., Akinlar, M.A.: Applicability of time conformable derivative to Wick-fractional-stochastic PDEs. Alex. Eng. J. 59(3), 1485–1493 (2020)
Ma, H.C., Yu, Y.D., Ge, D.J.: The auxiliary equation method for solving the Zakharov–Kuznetsov (ZK) equation. Comput. Math. Appl. 58(11–12), 2523–2527 (2009)
Malfliet, W., Hereman, W.: The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54, 563–568 (1996)
Mirzazadeh, M., Akinyemi, L., Senol, M., Hosseini, K.: A variety of solitons to the sixth-order dispersive \((3+1)\)-dimensional nonlinear time-fractional Schrödinger equation with cubic-quintic-septic nonlinearities. Optik 241, 1–15 (2021). https://doi.org/10.1016/j.ijleo.2021.166318
Osman, M.S., Baleanu, D., Tariq, K.U.H., Kaplan, M., Younis, M., Rizvi, S.T.R.: Different types of progressive wave solutions via the 2D-chiral nonlinear Schrödinger equation. Front. Phys. 8, 1–7 (2020). https://doi.org/10.3389/fphy.2020.00215
Rasheed, N.M., Al-Amr, M.O., Az-Zo’bi, E.A., Tashtoush, M.A., Akinyemi, L.: Stable optical solitons for the higher-order non-Kerr NLSE via the modified simple equation method. Mathematics 9(16), 1–12 (2021)
Raza, N., Javid, A.: Optical dark and dark-singular soliton solutions of \((1+2)\)-dimensional chiral nonlinear Schrodinger’s equation. Waves Random Complex Media 29, 496–508 (2019). https://doi.org/10.1080/17455030.2018.1451009
Rezazadeh, H., Ullah, N., Akinyemi, L., Shah, A., Mirhosseini-Alizamin, S.M., Chu, Y.M., Ahmad, H.: Optical soliton solutions of the generalized non-autonomous nonlinear Schrödinger equations by the new Kudryashov’s method. Results Phys. 24, 1–7 (2021a). https://doi.org/10.1016/j.rinp.2021.104179
Rezazadeh, H., Younis, M., Eslami, M., Bilal, M., Younas, U.: New exact traveling wave solutions to the \((2+1)\)-dimensional Chiral nonlinear Schrödinger equation. Math. Model. Nat. Phenom. 16, 1–15 (2021b). https://doi.org/10.1051/mmnp/2021001
Senol, M.: New analytical solutions of fractional symmetric regularized-long-wave equation. Revista Mexicana de Física 66(3), 297–307 (2020)
Sulem, C., Sulem, P.L.: The nonlinear Schrödinger equation. Springer-Verlag, New York (1999)
Tasbozan, O., Çenesiz, Y., Kurt, A.: New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. Eur. Phys. J. Plus 131(7), 1–14 (2016)
Vahidi, J., Zekavatmand, S.M., Rezazadeh, H., Inc, M., Akinlar, M.A., Chu, Y.M.: New solitary wave solutions to the coupled Maccari’s system. Results Phys. 21, 1–11 (2021). https://doi.org/10.1016/j.rinp.2020.103801
Vakhnenko, V.O., Parkes, E.J., Morrison, A.J.: A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos Solitons Fract. 17(4), 683–692 (2003)
Yan, Z.: Abundant families of Jacobi elliptic function solutions of the \((2+1)\)-dimensional integrable Davey–Stewartson-type equation via a new method. Chaos Solitons Fract. 18(2), 299–309 (2003)
Yang, X.J., Feng, Y.Y., Cattani, C., Inc, M.: Fundamental solutions of anomalous diffusion equations with the decay exponential kernel. Math. Methods Appl. Sci. 42(11), 4054–4060 (2019)
Zhang, S., Xia, T.: A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. Phys. Lett. A 363(5–6), 356–360 (2007)
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Akinyemi, L., Inc, M., Khater, M.M.A. et al. Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt Quant Electron 54, 191 (2022). https://doi.org/10.1007/s11082-022-03554-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-03554-6