Exact Solutions of the Lakshmanan–Porsezian–Daniel Equation
https://doi.org/10.56304/S2304487X21030020
Abstract
The Lakshmanan–Porsezian–Daniel equation, which is used to describe pulse propagation through optical fibers apart from the nonlinear Schrödiger equation, is considered. Assuming that the Lakshmanan–Porsezian–Daniel equation holds a solution in the form of a monochromatic wave with an envelope as a function of the travelling wave variable, this partial differential equation is reduced to the overdetermined system of two ordinary differential equations for the envelope of the monochromatic wave. The method to obtain consistency of the ordinary differential equation system, which is different from assuming that coefficients of one of the equations are zero, is presented. Using the consistency condition obtained, two periodic solutions for the envelope of the monochromatic wave are derived from the ordinary differential equation system. These solutions are expressed in terms of the Jacobi elliptic functions and contain two and three arbitrary constants, respectively. The existence criteria for these solutions are presented. It is shown that one of the presented solutions degenerates to a soliton solution for a particular value of one of the arbitrary constants.
About the Authors
A. A. Bayramukov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
A. A. Kutukov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
115409
Moscow
References
1. Alqahtani R. T., Babatin M. M., Biswas A., Bright optical solitons for Lakshmanan–Porsezian–Daniel model by semi-inverse variational principle, Optik. 2018. V. 154. P. 109–114.
2. Biswas A., Ekici M., Sonmezoglu A., Triki H., Majid F. B., Zhou Q., Moshokoa S. P., Mirzazadeh M., Belic M., Optical solitons with Lakshmanan–Porsezian–Daniel model using a couple of integration schemes, Optik. 2018. V. 158. P. 705–711.
3. Biswas A., Yildirim Y., Yasar E., Zhou Q., Moshokoa S. P., Belic M., Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method, Optik. 2018. V. 160. P. 24–32.
4. Jawad A. J. M., Abu-AlShaeer M. J., Biswas A., Zhou Q., Moshokoa S., Belic M., Optical solitons to Lakshmanan–Porsezian–Daniel model for three nonlinear forms, Optik. 2018. V. 160. P. 197–202.
5. Bansal A., Biswas A., Triki H., Zhou Q., Moshokoa S. P., Belic M., Optical solitons and group invariant solutions to Lakshmanan–Porsezian–Daniel model in optical fibers and PCF, Optik. 2018. V. 160. P. 86–91.
6. Zayed E. M. E., Alngar M. E. M., Biswas A., Yıldırım Y., Guggilla P., Khan S., Alzahrani A. K., Belic M. R., Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model, Optik. 2021. V. 233. P. 166385.
7. Kudryashov N. A., Optical solitons of model with integrable equation for wave packet envelope, Chaos, Solitons & Fractals. 2020. V. 141. P. 110325.
Review
For citations:
Bayramukov A.A., Kudryashov N.A., Kutukov A.A. Exact Solutions of the Lakshmanan–Porsezian–Daniel Equation. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2021;10(3):260-264. (In Russ.) https://doi.org/10.56304/S2304487X21030020
Views:
99
Email this article 