(3)Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations

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K. Hosseini ^a,∗, M. Inc ^b,∗, M. Shafiee ^a , M. Ilie ^a , A. Shafaroody ^c , A. Yusuf  ^b,d , M. Bayrame ^e

^a Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran 

^b Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey 

^c Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran 

^d Department of Mathematics, Federal University Dutse, 7156 Jigawa, Nigeria 

^e Department of Computer Engineering, Istanbul Gelisim University, Istanbul, Turkey Received 2 April 2019; 

Received in revised form 7 June 2019; accepted 21 July 2019 

Available online 5 August 2019

Abstract

   The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations (NLWWEs) in oceans through the invariant subspace scheme (ISS). In this respect, the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations (ODEs) such that the resulting systems can be efficiently handled by computer algebra systems. As an accomplishment, the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed. In the end, the stability analysis for the NLWWE is investigated through the linear stability scheme. © 2019 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license.(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Nonlinear water wave equations; Invariant subspace scheme; Exact solutions; Stability analysis.