New Solutions for the Resonant Nonlinear Schrödinger Equation with Anti-Cubic Nonlinearity

Year 2023, , 725 - 731, 28.09.2023

Ebru Cavlak Aslan , Leyla Gürgöze

https://doi.org/10.17798/bitlisfen.1289067

Abstract

In this work, the Resonant nonlinear Schrödinger equation (RNLSE) with anti-cubic nonlinearity is considered. The Jacobi elliptic function method (JEFM) has been employed on the RNLSE. The many new forms of dark, dark-bright, singular, combo-singular, bright-singular solitons and periodic solutions for governing model are reached. Furthermore, the graphics of solutions are presented.

Keywords

NLSE, Optical soliton, Soliton

References

• [1] Y. S. Kivshar and G. P. Agrawal, Optical solitons: From fibers to photonic crystals. Elsevier Science & Technology, 2003
• [2] A. Biswas and S. Konar, Introduction to non-Kerr law optical solitons. London, England: CRC Press, 2020.
• [3] E. Ulutas, “Travelling wave and optical soliton solutions of the Wick-type stochastic NLSE with conformable derivatives,” Chaos Solitons Fractals, vol. 148, no. 111052, p. 111052, 2021.
• [4] N. Cheemaa and M. Younis, “New and more general traveling wave solutions for nonlinear Schrödinger equation,” Waves Random Complex Media, vol. 26, no. 1, pp. 30–41, 2016.
• [5] A. M. Shahoot, K. A. E. Alurrfi, I. M. Hassan, and A. M. Almsri, “Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method,” Adv. Math. Phys., vol. 2018, pp. 1–11, 2018.
• [6] M. Mirzazadeh, R. T. Alqahtani, and A. Biswas, “Optical soliton perturbation with quadratic-cubic nonlinearity by Riccati-Bernoulli sub-ODE method and Kudryashov’s scheme,” Optik (Stuttg.), vol. 145, pp. 74–78, 2017.
• [7] K. Ayub, M. Y. Khan, and Q. Mahmood-Ul-Hassan, “Solitary and periodic wave solutions of Calogero–Bogoyavlenskii–Schiff equation via exp-function methods,” Comput. Math. Appl., vol. 74, no. 12, pp. 3231–3241, 2017.
• [8] W. B. Rabie and H. M. Ahmed, “Cubic-quartic solitons perturbation with couplers in optical metamaterials having triple-power law nonlinearity using extended F-expansion method,” Optik (Stuttg.), vol. 262, no. 169255, p. 169255, 2022.
• [9] N. A. Kudryashov, “Method for finding highly dispersive optical solitons of nonlinear differential equations,” Optik (Stuttg.), vol. 206, no. 163550, p. 163550, 2020.
• [10] N. A. Kudryashov, “Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations,” Appl. Math. Comput., vol. 371, no. 124972, p. 124972, 2020.
• [11] A. Zafar, M. Raheel, and A. Bekir, “Exploring the dark and singular soliton solutions of Biswas–Arshed model with full nonlinear form,” Optik (Stuttg.), vol. 204, no. 164133, p. 164133, 2020.
• [12] N. Z. Petrović and M. Bohra, “General Jacobi elliptic function expansion method applied to the generalized (3 + 1)-dimensional nonlinear Schrödinger equation,” Opt. Quantum Electron., vol. 48, no. 4, 2016.
• [13] T. A. Khalil, N. Badra, H. M. Ahmed, and W. B. Rabie, “Bright solitons for twin-core couplers and multiple-core couplers having polynomial law of nonlinearity using Jacobi elliptic function expansion method,” Alex. Eng. J., vol. 61, no. 12, pp. 11925–11934, 2022.
• [14] A. Biswas, A. Sonmezoglu, M. Ekici, A. S. Alshomrani, and M. R. Belic, “Highly dispersive singular optical solitons with Kerr law nonlinearity by Jacobi’s elliptic ds function expansion,” Optik (Stuttg.), vol. 192, no. 162954, p. 162954, 2019.
• [15] A. U. Awan, H. U. Rehman, M. Tahir, and M. Ramzan, “Optical soliton solutions for resonant Schrödinger equation with anti-cubic nonlinearity,” Optik (Stuttg.), vol. 227, no. 165496, p. 165496, 2021.
• [16] K. S. Nisar, K. K. Ali, Mustafa Inc, M. S. Mehanna, H. Rezazadeh, and L. Akinyemi, “New solutions for the generalized resonant nonlinear Schrödinger equation,” Results Phys., vol. 33, no. 105153, p. 105153, 2022.
• [17] S. Tarla, K. K. Ali, R. Yilmazer, and M. S. Osman, “New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method,” Opt. Quantum Electron., vol. 54, no. 2, 2022.
• [18] L. Gürgöze, “Exact Solutions With Jacobi Elliptic Function Method of Some Nonlineer Equations,” Firat University, 2022.
• [19] E. M. E. Zayed, R. M. A. Shohib, A. Biswas, Y. Yıldırım, F. Mallawi, and M. R. Belic, “Chirped and chirp-free solitons in optical fiber Bragg gratings with dispersive reflectivity having parabolic law nonlinearity by Jacobi’s elliptic function,” Results Phys., vol. 15, no. 102784, p. 102784, 2019.