Contents lists available at ScienceDirect Optik journal homepage: www.elsevier.com/locate/ijleo Original research article Optical solitons with differential group delay and dual-dispersion for Lakshmanan–Porsezian–Daniel model by extended trial function method Anjan Biswas a,b,c , Mehmet Ekici d, ⁎ , Abdullah Sonmezoglu d , M.M. Babatin b a Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA b Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia c Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa d Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey ARTICLE INFO OCIS: 060.2310 060.4510 060.5530 190.3270 190.4370Keywords: Solitons Dispersion Birefringence ABSTRACT This paper employs extended trial function method to extract soliton solutions to the vector- coupled Lakshmanan–Porsezian–Daniel model in birefringent fibers. The existence of these so- litons is guaranteed with the integrability criteria that are also presented. 1. Introduction Optical soliton perturbation is one of the fastest growing areas of research in the field of telecommunications industry. The engineering marvel in this field as it stands owes to several mathematical models that are studied in this context [1–20]. These plethora of models describe the dynamics in a variety of situations and circumstances. These models include the most visible non- linear Schrödinger's equation, Schrödinger-Hirota equation for dispersive solitons, Manakov equation for polarization mode dis- persion (PMD), Sasa-Satsuma equation for perturbed solitons and several others. This paper will address soliton study for PMD fibers with differential group delay with Lakshmanan–Porsezian–Daniel (LPD) model. It's scalar version is well studied and is well-known and well understood [1,3–8,13,14,16,19,20]. It's about time to turn the page for this model. The vector coupled version of LPD model to address birefringent fibers, without four-wave mixing (4WM) have been reported [2]. This paper will revisit the model for PMD fibers by the aid of extended trial function method. After a quick introduction to the system, with preliminary mathematical analysis, the scheme will retrieve soliton solutions. The integrability criteria will also be presented that guarantees the existence of these solitons and other such waves. 1.1. Governing model The dimensionless form of LPD model, with Kerr law nonlinearity, that has been studied in the past is given in the form https://doi.org/10.1016/j.ijleo.2018.06.012 Received 15 April 2018; Accepted 1 June 2018 ⁎ Corresponding author. E-mail address: ekici-m@hotmail.com (M. Ekici). Optik - International Journal for Light and Electron Optics 170 (2018) 512–519 0030-4026/ © 2018 Elsevier GmbH. All rights reserved. T