Vol.:(0123456789) Optical and Quantum Electronics ( 2020) 52:318 https://doi.org/10.1007/s11082-020-02412-7 1 3 Exact optical solitons to the perturbed nonlinear Schrödinger equation with dual‑power law of nonlinearity Nestor Savaissou 1  · B. Gambo 1  · Hadi Rezazadeh 2  · Ahmet Bekir 3  · Serge Y. Doka 1,4 Received: 16 January 2020 / Accepted: 15 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract In this paper, the perturbed nonlinear Schrödinger equation with dual-power law of nonlin- earity is studied by adopting four mathematical methods namely the Modifed Kudryashov method, the extended Tanh–Coth method, the modifed simple equation method and soliton ansatz method. As a results, a set of various types of solitons that contains dark, singular, dark–singular, bright optical solitons and other form of optical soliton solutions are obtained. Firstly, we solve the perturbed nonlinear Schrödinger equation by considering the dual power law parameter using the frst three integration methods and secondly we set this parameter equal to one in order, to solve the problem with the fourth method. The used methods in this paper present various applications in felds of nonlinear wave equations. Comparing our new results with well-known in literature are also given. Moreover, the graphical representations of the modulus of some optical soliton solutions and their 2-D profle are also depicted. Keywords Integrability · Waves · Nonlinear optics * Ahmet Bekir bekirahmet@gmail.com Nestor Savaissou savaissoun77@gmail.com Hadi Rezazadeh h.rezazadeh@ausmt.ac.ir 1 Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon 2 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran 3 Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030 Eskisehir, Turkey 4 Department of Physics, Faculty of Science, University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon