On the exact solutions to some system of complex nonlinear models

• Published in: Applied mathematics and nonlinear sciences Vol. 6; no. 1; pp. 29 - 42
• Main Authors: Sulaiman, Tukur Abdulkadir, Bulut, Hasan, Baskonus, Haci Mehmet
• Format: Journal Article
• Language: English
• Published: Beirut Sciendo 01.01.2021; De Gruyter Poland
• Subjects: 34A34; Davey-Stewartson equation; Maccari's system; soliton solutions; The extended ShEEM
• ISSN: 2444-8656; 2444-8656
• DOI: 10.2478/amns.2020.2.00007

In this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.