University of TabrizComputational Methods for Differential Equations2345-39829120210101Exact solutions of the combined Hirota-LPD equation with variable coefficients941161147710.22034/cmde.2020.31022.1466ENMehdiFazli AghdaeiDepartment of Mathematics,
Payame Noor University,
PO BOX 19395-3697, Tehran, Iran.HojatollahAdibiDepartment of Applied Mathematics,
faculty of Mathematics and Computer Sciences,
Amirkabir University of Technology,
No.424, Hafez Avenue, Tehran 15914, Iran.0000-0002-8167-5020Journal Article20181221In 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.https://cmde.tabrizu.ac.ir/article_11477_0d9481ffc78cd9c23911074e9a6501c3.pdf