Exact solutions of the combined Hirota-LPD equation with variable coefficients

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran.

2 Department of Applied Mathematics, faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran 15914, Iran.

Abstract

In this paper, we construct exact families of traveling wave (periodic wave, singular wave, singular periodic wave, singular-solitary wave and shock wave) solutions of a well-known equation of nonlinear PDE, the variable coefficients combined HirotaLakshmanan-Porsezian-Daniel (Hirota-LPD) equation with the fourth nonlinearity, which describes an important development, and application of soliton dispersion management experiment in nonlinear optics is considered, and as an achievement, a series of exact traveling wave solutions for the aforementioned equation is formally extracted. This nonlinear equation is solved by using the extended trial equation method (ETEM) and the improved tan(ϕ/2)-expansion method (ITEM). Meanwhile, the mechanical features of some families are explained through offering the physical descriptions. Analytical treatment to find the nonautonomous rogue waves are investigated for the combined Hirota-LPD equation.

Keywords

Computational Methods for Differential Equations
Volume 9, Issue 1
January 2021
Pages 94-116

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History

  • Receive Date: 21 December 2018
  • Revise Date: 25 December 2018
  • Accept Date: 11 November 2020

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