Investigation of highly dispersive solitons for the concatenation model with power law nonlinearity using the improved modified extended tanh-function method

Salah, Eman; Samir, Islam; Abo El-Dahab, Emad M.; Ahmed, Hamdy M.; Ammar, Medhat; Eslami, Mostafa

doi:10.22034/cmde.2024.61272.2632

Investigation of highly dispersive solitons for the concatenation model with power law nonlinearity using the improved modified extended tanh-function method

Document Type : Research Paper

Authors

¹ Department of Physics and Engineering Mathematics, Higher Institute of Engineering,El-Shorouk Academy, El-Shorouk, Cairo, Egypt.

² Department of Mathematics and Engineering Physics, Faculty of Engineering, Aim Shams University, Cairo, Egypt.

³ Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.

⁴ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

10.22034/cmde.2024.61272.2632

Abstract

This research examines the phenomenon of optical solitons in the framework of the dispersive concatenation model, which incorporates three established models: the Lakshmanan-Porsezian-Daniel equation (LPDE), the Hirota equation (HE), and the nonlinear Schr¨odinger equation (NLSE). This model describes the soliton transmission dynamics across transcontinental and transoceanic dynamics. The model provided is situated within the context of nonlinear optics, a branch of optics that deals with optical phenomena in materials where the response of the medium to light is nonlinear. The equation appears to be a generalized model that combines several well-known equations from nonlinear optics. These equations often emerge as simplified descriptions of specific nonlinear effects in various optical systems. They capture phenomena like self-focusing, self-phase modulation, and soliton propagation, among others. The improved modified extended tanh scheme (IMETS) is utilized to derive solitons and other solutions for the investigated model. Many types of solutions are extracted with the help of the IMETS. These solutions include dark, bright, and singular solitons, as well as Weierstrass elliptic and singular periodic solutions. The nature of the extracted solutions is illustrated by introducing both 2D and 3D graphical representations and setting the parameters with appropriate values.

Keywords

Main Subjects

Applications to the sciences

References

[1] A. Ankiewicz and N. Akhmediev, Higher-order integrable evolution equation and its soliton solutions, Physics Letters, 378(4) (2014), 358-361.

[2] A. Ankiewicz, Y. Wang, S. Wabnitz, and N. Akhmediev, Extended nonlinear Schr¨odinger equation with higher order odd and even terms and its rogue wave solutions, Physical Review E, 89(1) (2014), 012907.

[3] S. Arshed, A. Biswas, P. Guggilla, and A. S. Alshomrani, Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation with full nonlinearity, Physics Letters A, 384(26) (2020), 126191.

[4] S. Chen and Z. Yan, The Hirota equation: Darboux transform of the Riemann–Hilbert problem and higher-order rogue waves, Applied Mathematics Letters, 95 (2019), 65-71.

[5] A. Chowdury, D. Kedziora, A. Ankiewicz, and N. Akhmediev, Soliton solutions of an integrable nonlinear Schr¨odinger equation with quintic terms, Physical Review E, 90(3) (2014), 032922.

[6] A. Chowdury, D. Kedziora, A. Ankiewicz, and N. Akhmediev, Breather-to-soliton conversions described by the quintic equation of the nonlinear Schro¨dinger hierarchy, Physical Review E, 91(3) (2015), 032928.

[7] A. Chowdury, D. Kedziora, A. Ankiewicz, and N. Akhmediev, Breather solutions of the integrable quintic nonlinear Schr¨odinger equation and their interactions, Physical Review E, 91(2) (2015), 022919.

[8] O. El-shamy, R. El-barkoki, H. M. Ahmed, W. Abbas, and I. Samir, Exploration of new solitons in optical medium with higher-order dispersive and nonlinear effects via improved modified extended tanh function method, Alexandria Engineering Journal, 68 (2023), 611-618.

[9] O. Gonz´alez-Gaxiola and A. Biswas, Optical solitons with Radhakrishnan–Kundu–Lakshmanan equation by Laplace–Adomian decomposition method, Optik, 179 (2019), 434–42.

[10] H. H. Hussein, H. M. Ahmed, and W. Alexan, Analytical soliton solutions for cubic-quartic perturbations of the Lakshmanan-Porsezian-Daniel equation using the modified extended tanh function method , Ain Shams Engineering Journal, 15(3) (2024), 102513.

[11] A. Jhangeer, H. Rezazadeh, and A. Seadawy, A study of travelling, periodic, quasiperiodic and chaotic structures of perturbed Fokas–Lenells model, Pramana, 95 (2021), 1–11.

[12] N. A. Kudryashov, On traveling wave solutions of the Kundu–Eckhaus equation, Optik, 224 (2020), 165500.

[13] I. Onder, A. Secer, M. Ozisik, and M. Bayram, Investigation of optical soliton solutions for the perturbed GerdjikovIvanov equation with full-nonlinearity, Heliyon, 9(2) (2023), e13519.

[14] W. B. Rabie, H. M. Ahmed, A. R. Seadawy, A. Althobaiti, The higher-order nonlinear Schrodinger’s dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity via dispersive analytical soliton wave solutions, Optical and Quantum Electronics, 53 (2021), 1-25.

[15] I. Samir, N. Badra, A. R. Seadawy, H. M. Ahmed, A. H. Arnous, Computational extracting solutions for the perturbed Gerdjikov-Ivanov equation by using improved modified extended analytical approach, Journal of Geometry and Physics, 176 (2022), 104514.

[16] I. Samir, H. M. Ahmed, M. Mirzazadeh, and H. Triki, Derivation new solitons and other solutions for higher order Sasa–Satsuma equation by using the improved modified extended tanh scheme, Optik, 274 (2023), 170592.

[17] A. R. Seadawy, Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma, Computers & Mathematics with Applications, 67(1) (2014), 172–180.

[18] A. R. Seadawy, K. K. Ali, and R. Nuruddeen, A variety of soliton solutions for the fractional Wazwaz-BenjaminBona-Mahony equations, Results in Physics, 12 (2019), 2234–2241.

[19] A. R. Seadawy, M. Arshad, and D. Lu, The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows, Chaos, Solitons & Fractals, 139 (2020), 110141.

[20] A. R. Seadawy, S. T. Rizvi, I. Ali, M. Younis, K. Ali, M. Makhlouf, and A. Althobaiti, Conservation laws, optical molecules, modulation instability and Painlev´e analysis for the Chen–Lee–Liu model, Optical and Quantum electronics, 53 (2021), 1–15.

[21] A. R. Seadawy and B. A. Alsaedi, Soliton solutions of nonlinear Schr¨odinger dynamical equation with exotic law nonlinearity by variational principle method, Optical and Quantum Electronics, 56(4) (2024), 700.

[22] A. R. Seadawy and B. Alsaedi, Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrodinger equation with polynomial law nonlinearity, AIMS Math, 9(3) (2024), 6336–6367.

[23] E. M. Zayed, K. A. Gepreel, M. El-Horbaty, A. Biswas, Y. Yıldırım, H. Triki, and A. Asiri, Optical Solitons for the Dispersive Concatenation Model, Contemporary Mathematics, 4(3) (2023), 592–611.