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Optical solitons in Bragg gratings fibers for the nonlinear (2+1)-dimensional Kundu–Mukherjee–Naskar equation using two integration schemes

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Abstract

The current work handles for the first time, dispersive optical solitons in fiber Bragg gratings for the nonlinear (2+1)-dimensional Kundu–Mukherjee–Naskar equation. Two integration schemes, namely, the modified Kudryashov’s approach and the addendum to Kudryashov’s methodology are applied. Dark and bright soliton solutions as long as explicit solutions are obtained. Also, combo bright-singular solutions are introduced.

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References

  • Arshed, S., Biswas, A., Guggilla, P., Alshomrani, A.S.: Optical solitons for Radhakrishnan-Kundu-Lakshmanan equation with full nonlinearity. Phys. Lett. A 384, 126191 (2020)

    Article  MathSciNet  Google Scholar 

  • Biswas, A.: Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis. Optik 171, 217–220 (2018)

    Article  ADS  Google Scholar 

  • Biswas, A., Vega-Guzman, J., Mahmood, M.F., Khan, S., Zhou, Q., Moshokoa, S.P., Belic, M.: Solitons in optical fiber Bragg gratings with dispersive reflectivity. Optik. 182, 119–123 (2019)

    Article  ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Solitons in optical fiber Bragg gratings with dispersive reflectivity by extended trial function method. Optik. 182, 88–94 (2019)

    Article  ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Optical solitons in fiber Bragg gratings with dispersive reflectivity for parabolic law nonlinearity by extended trial function method. Optik. 183, 595–601 (2019)

    Article  ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Optical solitons in fiber Bragg gratings with dispersive reflectivity for quadratic-cubic nonlinearity by extended trial function method. Optik. 185, 50–56 (2019)

    Article  ADS  Google Scholar 

  • Biswas, A., Vega-Guzman, J., Mahmood, M.F., Ekici, M., Zhou, Q., Moshokoa, S.P., Belic, M.R.: Optical solitons in fiber Bragg gratings with dispersive reflectivity for parabolic law nonlinearity using undetermined coefficients. Optik. 185, 39–44 (2019)

    Article  ADS  Google Scholar 

  • Chen, S.J., Ma, W.X., Lü, X.: Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation. Commun. Nonlinear Sci. Numer. Simul. 83, 105135 (2020)

    Article  MathSciNet  Google Scholar 

  • Chen, S.J., Lü, X., Tang, X.F.: Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients. Commun. Nonlinear Sci. Numer. Simul. 95, 105628 (2021)

    Article  MathSciNet  Google Scholar 

  • Chen, S.J., Lü, X., Li, M.G., Wang, F.: Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations. Phys. Scr. 96, 095201 (2021)

    Article  ADS  Google Scholar 

  • Ekici, M., Sonmezoglu, A., Biswas, A., Belic, M.R.: Optical solitons in (2+1)-Dimensions with Kundu–Mukherjee–Naskar equation by extended trial function scheme. Chin. J. Phys 57, 72–77 (2019)

    Article  Google Scholar 

  • He, X.J., Lü, X., Li, M.G.: Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. Anal. Math. Phys. 11, 1–24 (2021)

    Article  Google Scholar 

  • Kudryashov, N.A.: First integrals and solutions of the traveling wave reduction for the Triki–Biswas equation. Optik. 185, 275–281 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: General solution of traveling wave reduction for the Kundu–Mukherjee–Naskar equation. Optik. 186, 22–27 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik. 206, 163550 (2020)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: First integrals and general solution of the complex Ginzburg–Landau equation. Appl. Math. Comput. 386, 125407 (2020)

    MathSciNet  MATH  Google Scholar 

  • Kudryashov, N.A., Safonova, D.V., Biswas, A.: Painleve analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation. Reg. Chaot. Dyn. 24, 607614 (2019)

    MathSciNet  MATH  Google Scholar 

  • Lü, X., Chen, S.J.: Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dynam. 103(1), 947–977 (2021)

    Article  Google Scholar 

  • Lü, X., Ma, W.X.: Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dynam. 85, 1217–1222 (2016)

    Article  MathSciNet  Google Scholar 

  • Lü, X., Chen, S.T., Ma, W.X.: Constructing lump solutions to a generalized Kadomtsev–Petviashvili–Boussinesq equation. Nonlinear Dynam. 86, 523–534 (2016)

    Article  MathSciNet  Google Scholar 

  • Lü, X., Hua, Y.F., Chen, S.J., Tang, X.F.: Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painleve analysis, soliton solutions, Backlund transformation, Lax pair and infinitely many conservation laws. Commun. Nonlinear Sci. Numer. Simul. 95, 105612 (2021)

    Article  Google Scholar 

  • Trik, H., Benlalli, A., Zhou, Q., Biswas, A., Yıldırım, Y., Alzahrani, A.K., Belic, M.R.: Gray optical dips of Kundu–Mukherjee–Naskar model. Phys. Lett. A. 401, 127341 (2021)

    Article  MathSciNet  Google Scholar 

  • Xia, J.W., Zhao, Y.W., Lü, X.: Predictability, fast calculation and simulation for the interaction solutions to the cylindrical Kadomtsev-Petviashvili equation. Commun. Nonlinear Sci. Numer. Simul. 90, 105260 (2020)

    Article  MathSciNet  Google Scholar 

  • Xu, H.N., Ruan, W.Y., Zhang, Y., Lü, X.: Multi-exponential wave solutions to two extended Jimbo–Miwa equations and the resonance behavior. Appl. Math. Lett. 99, 105976 (2020)

    Article  MathSciNet  Google Scholar 

  • Yıldırım, Y.: Optical solitons to Kundu–Mukherjee–Naskar model in birefringent fibers with trial equation approach. 183, 1026–1031 (2019)

  • Yıldırım, Y.: Optical solitons to Kundu–Mukherjee–Naskar model in birefringent fibers with modified simple equation approach. Optik 184, 121–127 (2019)

    Article  ADS  Google Scholar 

  • Yıldırım, Y.: Optical solitons to Kundu–Mukherjee–Naskar model with trial equation approach. Optik. 183, 1061–1065 (2019)

    Article  ADS  Google Scholar 

  • Yıldırım, Y.: Optical solitons to Kundu-Mukherjee-Naskar model with modified simple equation approach. Optik 184, 247–252 (2019)

    Article  ADS  Google Scholar 

  • Yıldırım, Y., Mirzazadeh, M.: Optical pulses with Kundu–Mukherjee–Naskar model in fiber communication systems. Chinese J. Phys. 64, 183–193 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  • Yıldırım, Y., Biswas, A., Ekici, M., Triki, H., Gaxiola, O.G., Alzahrani, A.K., Belic, M.R.: Optical solitons in birefringent fibers for Radhakrishnan–Kundu–Lakshmanan equation with five prolific integration norms. Optik 208, 164550 (2020)

    Article  ADS  Google Scholar 

  • Yin, Y.H., Chen, S.J., Lü, X.: Study on localized characteristics of lump and interaction solutions to two extended Jimbo-Miwa equations. Chin. Phys. B. 29, 120502 (2020)

    Article  ADS  Google Scholar 

  • Zayed, E.M.E., Gepreel, K.A., Alngar, M.E.M.: Addendum to Kudryashov’s method for finding solitons in magneto-optics waveguides to cubic-quartic NLSE with Kudryashov’s sextic power law of refractive index. Optik. 230, 166311 (2021)

  • Zayed, E.M.E., Shohib, R.M.A., Gepreel, K.A., El-Horbaty, M.M., Alngar, M.E.M.: Cubic-quartic optical soliton perturbation Biswas-Milovic equation with Kudryashov’s law of refractive index using two integration methods Optik. 239, 166871 (2021)

  • Zayed, E.M.E., Nofal, T.A., Gepreel, K.A., Shohib, R.M.A., Alngar, M.E.M.: Cubic-quartic optical soliton solutions in fiber Bragg gratings with Lakshmanan–Porsezian–Daniel model by two integration schemes. Opti. Quantum Electron. 53, 1–17 (2021)

    Article  Google Scholar 

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Correspondence to Mohamed E. M. Alngar.

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Zayed, E.M.E., Shohib, R.M.A. & Alngar, M.E.M. Optical solitons in Bragg gratings fibers for the nonlinear (2+1)-dimensional Kundu–Mukherjee–Naskar equation using two integration schemes. Opt Quant Electron 54, 16 (2022). https://doi.org/10.1007/s11082-021-03385-x

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