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The nonlinear Schrödinger equation with polynomial law nonlinearity: localized chirped optical and solitary wave solutions

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Abstract

In this paper, we will find the chirped solitons (CS) solutions to the nonlinear schrödinger’s equation (NLSE) under polynomial nonlinearity with spatio temporal dispersion (STD) and group velocity dispersion (GVD). We will find CS with Jacobi elliptic functions (JEF). We will also get some new solitary waves (SW) like bright, dark, kink, periodic, hyperbolic, and other solutions. The dynamical behaviour for these waves will also be discussed along with constraint conditions.

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References

  • Alka, A. Goyal, R. Gupta, C. N. Kumar, and T. S. Raju, Chirped femtosecond solitons and double kink solitons in the cubic-quintic NLSE with self-steepening and self-frequency shift, Phys. Rev. A, 84 063830 (2011)

  • Aly, R.: Seadawy, Asghar Ali, Saad Althobaiti, and Khaled El-Rashidy, Construction of abundant novel analytical solutions of the space-time fractional nonlinear generalized equal width model via Riemann-Liouville derivative with application of mathematical methods, Open. Physics 19, 657–668 (2021)

  • Aly, R.: Seadawy, Dianchen Lu, Naila Nasreen and Shamila Nasreen, Structure of optical solitons of resonant Schrodinger equation with quadratic cubic nonlinearity and modulation instability analysis. Physica A 534, 1221 (2019)

  • Aly R. Seadawy, Asim Zafar and M. Raheel, On dark and singular solitons and other solutions with anti-cubic law of nonlinearity in optical metamaterials, Int. J. Modern Phys. B 34, No. 20 (2020) 2050186 (14 pages)

  • Aly R. Seadawy, Syed T. R. Rizvi and Saad Althobaiti, Chirped Periodic and Solitary Waves for Improved Perturbed Nonlinear Schrödinger Equation with Cubic Quadratic Nonlinearity, Fractal Fract. 2021, 5, 234

  • Aly R. Seadawy, Syed T. R. Rizvi, M. Younis, M. Aamir Ashraf, Breather, multi wave, periodic cross kink, M shaped and interactions solutions for perturbed NLSE with quadratic cubic nonlinearity, Opt. Q. Electron. 53:631 (2021)

  • Bilal, M., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: Highly dispersive optical solitons and other solutions for Radhkrishnan Kundu Lakshmanan equation in birefringent fibers by an efficient computational technique. Opt. Quant. Electron. 53, 435 (2021)

    Article  Google Scholar 

  • Desaix, M., Helczynski, L., Anderson, D., Lisak, M.: Propagation properties of CS pulses in optical nonlinear Kerr media. Phys. Rev. E 65, 056602 (2002)

    Article  ADS  Google Scholar 

  • Eslami, M.: SW solutions for perturbed NLSE with Kerr law nonlinearity under the DAM. Optik 126, 1312–1317 (2015)

    Article  ADS  Google Scholar 

  • Filiz, A., Sonmezoglu, A., Ekici, M.: F-expansion method and new exact solutions of the schrödinger-KdV equation. Sci. World J. 2014, 3928877 (2014)

    Article  Google Scholar 

  • Gawarai Dieu-donne, Malwe Boudoue Hubert, Aly Seadawy, Temwa Etienne, Gambo Betchewe and Serge Y. Doka, Chirped soliton solutions of Fokas-Lenells equation with perturbation terms and the effect of spatio-temporal dispersion in the modulational instability analysis, The European Physical Journal Plus volume 135, Article number: 212 (2020)

  • Ghanbari, B., Nisar, K. S., Aldhaifallah, M.: Abundant SW solutions to an extended NLSE with conformable derivative using an efficient integration method, Adv. Differ. Equ., 328(2020)

  • Goyal, A., Sharma, V.K., Raju, T.S., Kumar, C.N.: Chirped double-kink and fractional-transform solitons in an optical gain medium with two-photon absorption. J. Mod. Opt. 61, 315–321 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  • Iftikhar Ahmed, Aly R. Seadawy, Dianchen Lu, The interaction of W-shaped rational solitons with kink wave for the nonlinear Schrodinger equation with anti-cubic nonlinearity, Modern Phys. Lett. B, 34, No. 12 (2020) 2050122 (8 pages)

  • Khaled El-Rashidy, Aly R. Seadawy, Saad Althobaiti, and M. M. Makhlouf, Investigation of interactional phenomena and multi wave solutions of the quantum hydrodynamic Zakharov-Kuznetsov model, Open Phys. 2021; 19: 91-99

  • Özgül, S., Turan, M., Yıldırım, A.: Exact traveling wave solutions of perturbed NLSE with Kerr law nonlinearity. Optik 123, 2250–2253 (2012)

    Article  ADS  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Younis, M., Ahmad, S., Ali, K.: Weierstrass and Jacobi elliptic functions with some new dromions to Maccari system. Int. J. Mod. Phy. B 35(25), 2150257 (2021)

    Article  ADS  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Younis, M., Ahmad, N., Zaman, S.: Optical dromions for perturbed fractional nonlinear Schrodinger equation with conformable derivatives. Opt. Quant. Electron. 53, 477 (2021)

    Article  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Bibi, I., Younis, M.: Chirped and chirp-free OS for Heisenberg ferromagnetic spin chains model. Mod. Phys. Lett. B 35(8), 2150139 (2021)

    Article  ADS  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Ashraf, M.A., Younis, M., Khailq, A.: Rogue, multiwave, homoclinic breather, M-shaped rational and periodic kink solutions for a nonlinear model describing vibrations. Results in Phys. 29, 104654 (2021)

    Article  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Ashraf, M.A., Bashir, A., Younis, M., Baleanu, D.: Multiwave, homoclinic breather, M-shaped rational and other solitary wave solutions for coupled Higgs equation. Special topics, The European Physical Journal (2021)

    Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Ahmed, S., Younis, M., Ali, K.: Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation. Chaos; Solitons and Fractals 151, 111251 (2021)

    Article  Google Scholar 

  • A. R. Seadawy, S. T. R. Rizvi, M. Younis, M. Aamir Ashraf, Breather, multi-wave, periodic-cross kink, M-shaped and interactions solutions for perturbed NLSE with quadratic cubic nonlinearity, Opt. Q. Electron., 53: 631 (2021)

  • Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S.: Chirped periodic and solitary waves for improved perturbed nonlinear Schrodinger equation with cubic quadratic nonlinearity. Fractal and Fract. 5(4), 234 (2021)

    Article  Google Scholar 

  • Taghreed G. Sugati, Aly R. Seadawy, R. A. Alharbey, W. Albarakati, Nonlinear physical complex hirota dynamical system: Construction of chirp free optical dromions and numerical wave solutions, Chaos, Solitons and Fractals 156 (2022) 111788

  • Triki, H., Porsezian, K., Choudhuri, A., Dinda, P.T.: Chirped solitary pulses for a nonic NLSE on a continuous-wave background. Phys. Rev. A 93, 063810 (2016)

    Article  ADS  Google Scholar 

  • Younis, M., Bilal, M., Rehman, S.U., Seadawy, A.R., Rizvi, S.T.R.: Kinetics of phase separation in Fe-Cr-X(X=Mo, Cu) ternary alloys; a dynamical wave study. Int. J. Mod. Phy. B. 35(21), 2150220 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  • Younis, M., Seadawy, A.R., Baber, M.Z., Rizvi, S.T.R., Iqbal, M.S.: Diverse acoustic wave propagation to conformable time-space fractional KP equation arising in dusty plasma. Commun. Theoretical Phys. 73, 115004 (2021)

    Article  ADS  Google Scholar 

  • Zhou, Q.: Analytic study on OS in a Kerr-law medium with an imprinted parity-time-symmetric mixed linear-nonlinear lattice, Proc. Rom. Acad., Ser. B, 18 (2017) 223-230

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Authors and Affiliations

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

    N. Aziz, K. Ali, M. Sohail & S. T. R. Rizvi

  2. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

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  1. N. Aziz
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  2. Aly R. Seadawy
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  3. K. Ali
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  4. M. Sohail
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  5. S. T. R. Rizvi
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Correspondence to Aly R. Seadawy.

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Aziz, N., Seadawy, A.R., Ali, K. et al. The nonlinear Schrödinger equation with polynomial law nonlinearity: localized chirped optical and solitary wave solutions. Opt Quant Electron 54, 458 (2022). https://doi.org/10.1007/s11082-022-03831-4

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