Analytical Rational Solitons of the Modified Lakshmanan-Porsezian-Daniel Equation

Year 2023, Volume: 6 Issue: 2, 53 - 64, 01.07.2023

İlker Burak Giresunlu , Bengi Yıldız

https://doi.org/10.32323/ujma.1289530

Abstract

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is studied. New analytical rational solitons to the LPD equation are presented by an ansatz method. Wave solutions of three types, such as parabolic, trigonometric and hyperbolic function solutions have been retrieved. All solutions are plotted in 3D to enhance the understanding of their physical characteristics. These simulations, which represent the behavior of the resulting hyperbolic, parabolic and trigonometric solitons, are provided by choosing different appropriate values of the parameters.

Keywords

Hyperbolic soliton, Lakshmanan-Porsezian-Daniel equation, Parabolic soliton, Trigonometric soliton

References

• [1] G. Akram, M. Sadaf, S. Arshed, F. Sameen, Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan-Porsezian-Daniel model by generalized projective Riccati equations method, Optik, (2021), Article ID 167051, 241.
• [2] G. Akram, M. Sadaf, M. Dawood, Optical solitons for Lakshmanan-Porsezian-Daniel equation with Kerr law non-linearity using improved $\tan\left(\frac{\psi(\eta)}{2}\right)$-expansion technique, Results in Physics, (2021), Article ID 104758, 29.
• [3] A. Al Qarni, A. Alshaery, H. Bakodah, Optical solitons for the Lakshmanan-Porsezian-Daniel model by collective variable method, Results in Optics, (2020), Article ID 100017, 1.
• [4] A. Biswas, Y. Yildirim, E. Yasar, Q. Zhou, S.P. Moshokoa, M. Belic, Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method, Optik, 160 (2018), 24–32.
• [5] J. Vega-Guzman, R. T. Alqahtani, Q. Zhou, M. F. Mahmood, S. P. Moshokoa, M. Z. Ullah, A. Biswas, M. Belic, Optical solitons for Lakshmanan– Porsezian–Daniel model with spatio-temporal dispersion using the method of undetermined coefficients, Optik, 144 (2017), 115–123.
• [6] Y. Yang, T. Suzuki, X. Cheng, Darboux transformations and exact solutions for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation, Appl. Math. Lett., (2020), Article ID 105998, 99.
• [7] X. H. Wu, Y. T. Gao, X. Yu, C. C. Ding, L. Q. Li, Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation, M. Chaos, Solitons & Fractals, 162 (2022), Article ID 112399.
• [8] Y. Ye, C. Hou, D. Cheng, S. Chen, Rogue wave solutions of the vector Lakshmanan–Porsezian–Daniel equation, Phys. Lett. A, 384 (11) (2020), Article ID 126226.
• [9] G. Akram, M. Sadaf, M. A. U. Khan, Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method, Optik, 251 (2022), Article ID 168163.
• [10] M. Lakshmanan, K. Porsezian, M. Daniel, Effect of discreteness on the continuum limit of the Heisenberg spin chain, Phys. Lett. A, 133 (9) (1988), 483-488.
• [11] N. A. Kudryashov, The Lakshmanan–Porsezian–Daniel model with arbitrary refractive index and its solution, Optik, (2021), Article ID 167043, 241.
• [12] J. Y. Yang, W. X. Ma, Z. Qin, Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation, Anal. Math. Phys., 8 (2018), 427–436.