Document Type : Research Paper
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
Department of Mathematics, University of Bonab, Bonab, Iran.
In this work, we established some exact solutions for the $(1+1)$-dimensional and $(2+1)$-dimensional fifth-order integrable equations ($(1+1)$D and $(2+1)$D FOIEs) which is considered based on the improved $\tanh(\phi(\xi)/2)$ expansion method (IThEM), by utilizing Maple software. We obtained new periodic solitary wave solutions. The obtained solutions include soliton, periodic, kink, kink-singular wave solutions. Comparing our new results with Wazwaz results, namely, the Hereman-Nuseri method shows that our results give further solutions. Many other such types of nonlinear equations arise in fluid dynamics, plasma physics, and nonlinear physics.