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Bäcklund transformation method; Kudryashov method; new auxiliary ordinary differential equation; Lakshmanan–Porsezian–Daniel equation; Kerr nonlinearity; exact solutions

This paper examines new travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) model with Kerr nonlinearity using Bäcklund transformation method based on Riccati equation, Kudryashov method and a new auxiliary ordinary differential equation (ODE). The three methods are adequately utilised, and some new rational-type hyperbolic and trigonometric function solutions are derived in different shapes for the aforementioned model. We confirm that our methods are more efficient than the other methods and it might be used in many other such types of nonlinear equations arising in the basic fabric of communications network technology and nonlinearoptics.

HADI REZAZADEH¹ DIPANKAR KUMAR^{2 3} AHMAD NEIRAMEH⁴ MOSTAFA ESLAMI⁵ MOHAMMAD MIRZAZADEH⁶

1. Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran
2. Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, Japan
3. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh
4. Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran
5. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
6. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran

Published

10 February 2020

Manuscript received

28 June 2018

Manuscript revised

19 September 2019

Accepted

25 September 2019

Early published

Unedited version published online

Final version published online

7 February 2020