EXACT SOLUTIONS OF THE LAKSHMANAN – PORSEZIAN – DANIEL EQUATION: Exact solutions of the Lakshmanan – Porsezian – Daniel equation

Gaukhar N. Shaikhova; Araylym M. Syzdykova; Gaziz Kudaibergenov

doi:10.52575/2687-0959-2022-54-1-15-20

Authors

Gaukhar N. Shaikhova L. N. Gumilyov Eurasian National University http://orcid.org/0000-0002-0819-5338
Araylym M. Syzdykova L. N. Gumilyov Eurasian National University http://orcid.org/0000-0002-8999-6566
Gaziz Kudaibergenov L. N. Gumilyov Eurasian National University

DOI:

https://doi.org/10.52575/2687-0959-2022-54-1-15-20

Keywords:

Lakshmanan-Porsezian-Daniel equation, AKNS, Lax pair, sine-cosine method, hyperbolic tangent method

Abstract

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This equation is integrable and admits Lax pair. The LPD equation is the generalization of the nonlinear Schrodinger (NLS) equation and described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using the sine-cosine method and the hyperbolic tangent method a variety of new exact solutions are obtained. These methods are effective tools for searching exact solutions of nonlinear partial differential equations in mathematical physics. The obtained solutions are found to be important for the explanation of some practical physical problems.

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Author Biographies

Gaukhar N. Shaikhova, L. N. Gumilyov Eurasian National University

PhD, associate professor, Department of General and Theoretical Physics, L. N. Gumilyov Eurasian National University,
Nur-Sultan, Kazakhstan

Araylym M. Syzdykova, L. N. Gumilyov Eurasian National University

Researcher at L. N. Gumilyov Eurasian National University,
Nur-Sultan, Kazakhstan

Gaziz Kudaibergenov, L. N. Gumilyov Eurasian National University

undergraduate student, Department of General and Theoretical Physics, L. N. Gumilyov Eurasian National University,
Nur-Sultan, Kazakhstan

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EXACT SOLUTIONS OF THE LAKSHMANAN – PORSEZIAN – DANIEL EQUATION