Mathematics and Computational Sciences

Extended rational techniques to resonant nonlinear Schrodinger equation

Document Type : Original Article

Authors

Nikan Ahmadi Karchi 1
mohammad bagher ghaemi 1
Javad Vahidi 2

1 School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran

2 School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran, Iran.

https://doi.org/10.30511/mcs.2024.2026960.1164
Abstract
This paper studies advanced mathematical methods like sin-cos and sinh-cosh approaches
to find precise solutions by considering inter-modal dispersion and spatio-temporal dynamics with kerr
law nonlinearity in the Resonant shrödinger equation. These methods are useful for solving nonlinear
partial differential equations. To obtain the ordinary differential equation for the traveling wave solution,
we initially deal with the general partial differential equation (PDE). Then, a series of optical soliton
solutions, including cusp and dark solitons, are derived for the Resonant shrödinger equation using this
effective approach.

Keywords

Sine-cosine and sinh-cosh methods
Solition solution with complex structure
Resonant nonlinear Schrodinger equation
Optics

Subjects

[1] Ahmadi Karchi, N., Ghaemi, M. B., Vahidi, J. (2024). Precise solutions to the hirota equation and Hirota-Maccari system by using the extended rational methods. Int. J. Nonlinear Anal. Appl.15(2), 11–27.
[2] AL-saedi, A. A., Nikan, O., Avazzadeh, Z., Lopes, A. M. (2023). Solitary wave propagation of the generalized Rosenau–Kawahara–RLW equation in shallow water theory with surface tension. Symmetry, 15(11), 1980.
[3] Avazzadeh, Z., Nikan, O., Machado, J. A. T. (2020). Solitary wave solutions of the generalized Rosenau-KdV-RLW equation. Mathematics, 8(9), 1601.
[4] Bulut, H., Sulaiman, T. A., Baskonus, H. M. (2018). Optical solitons to the resonant nonlinear Schrodinger equation with both spatio-temporal and inter-modal dispersions under kerr law nonlinearity. Optik, 163, 49–55.
[5] Guo, T., Nikan, O., Qiu, W., Xu, D. (2023). Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics. Commun. Nonlinear Sci. Numer. Simul.117, 106989.
[6] Inc, M., Aliyu, A. I., Yusuf, A. (2017). Solitons and conservation laws to the resonance nonlinear Shrodinger s equation with both spatio-temporal and inter-modal dispersions. Optik 142, 509–522.
[7] Karchi, N. A., Ghaemi, M. B., Vahidi, J. (2023).New precise solutions to the Bogoyavlenskii equation by extended rational techniques. Int. J. Mod. Phys. B. 37(21), 2350203.
[8] Li, M., Nikan, O., Qiu, W., Xu, D. (2022).An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows. Eng. Anal. Bound. Elem. 144, 44–54.
[9] Muniyappan, A., Manikandan, K., Saparbekova, A., Serikbayev, N. (2024) Exploring the dynamics of dark and singular solitons in optical fibers using extended rational Sinh–Cosh and sine–Cosine methods. Symmetry. 16(5), 561.
[10] Nguyen, A. T., Nikan, O., Avazzadeh, Z. (2024). Traveling wave solutions of the nonlinear Gilson–Pickering equation in crystal lattice theory. J. Ocean Eng. Sci. 9(1), 40-49.
[11] Nikan, O., Avazzadeh, Z. (2021). A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics. Appl. Math. Comput. 401, 126063.
[12] Nikan, O., Avazzadeh, Z. (2022). A locally stabilized radial basis function partition of unity technique for the sine–Gordon system in nonlinear optics. Math. Comput. Simul. 199, 394–413.
[13] Nikan, O., Avazzadeh, Z. (2021). An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory. Eng. Anal. Bound. Elem. 130, 268–285
[14] Nikan, O., Avazzadeh, Z., Rasoulizadeh, M. N. (2021). Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory. Nonlinear Dyn. 106(1).
[15] Nikan, O., Avazzadeh, Z., Rasoulizadeh, M. N. (2022). Soliton wave solutions of nonlinear mathematical models in elastic rods and bistable surfaces. Eng. Anal. Bound. Elem. 143, 14–27.
[16] Nikan, O., Golbabai, A., Nikazad, T. (2019). Solitary wave solution of the nonlinear KdV-Benjamin-Bona-Mahony-Burgers model via two meshless methods. Eur. Phys. J. Plus. 134,1–14.
[17] Nikan, O., Yang, Y., Avazzadeh, Z. (2023). Numerical modeling of the ion-acoustic solitary waves arising in nonlinear dispersive system. Math. Methods Appl. Sci.
[18] Qiao, L., Nikan, O., Avazzadeh, Z. (2023). Some efficient numerical schemes for approximating the nonlinear two-space dimensional extended Fisher-Kolmogorov equation. Applied Numerical Mathematics. 185, 466–482.
[19] Rashidinia, J., Karamipour, Y., Nikan, O. (2021). The meshless methods for numerical solution of the nonlinear klein-gordon equation. TWMS J. of Apl. Eng. Math. 11(2), 436.
[20] Rasoulizadeh, M. N., Nikan, O., Avazzadeh, Z. (2021). An efficient local meshless method for the equal width equation in fluid mechanics. Eng. Anal. Bound. Elem. 131, 258–268.
[21] Rasoulizadeh, M. N., Nikan, O., Avazzadeh, Z. (2021). The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation. Math. Sci. 15(4), 365–376 (2021)
[22] Vahidi, J., Zabihi, A., Rezazadeh, H., Ansari, R. (2021). New extended direct algebraic method for the resonant nonlinear Schrodinger equation with kerr law nonlinearity. Optik. 227, 165936.
[23] Zayed, E. M., Shohib, R. M. (2018). Solitons and other solutions to the resonant nonlinear Schrodinger equation with both spatio-temporal and inter-modal dispersions using different techniques. Optik. 158, 970–984.
Mathematics and Computational Sciences
Volume 5, Issue 2
Spring 2024
Pages 49-62

  • Receive Date 20 April 2024
  • Revise Date 10 June 2024
  • Accept Date 21 June 2024

Home

Submit Manuscript

Reviewers

Contact Us