(7)New solitary wave structures to the (3 + 1) dimensional Kadomtsev–Petviashvili and Schrödinger equation

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Hasan Bulut ^a,∗, Emine Nesligül Aksan ^b,  Miraç Kayhan ^b,  Tukur Abdulkadir Sulaıman ^a,c

^a Department of Mathematics, University of Fırat, Elazı˘g, Turkey 

^b Department of Mathematics, University of ˙Inonu, Malatya, Turkey 

^c Department of Mathematics, Federal University Dutse, Jigawa, Nigeria 

Received 30 November 2018; received in revised form 7 June 2019; accepted 9 June 2019 

Available online 12 June 2019 

Abstract 

    The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this paper, an efficient mathematical technique, namely; the sine-Gordon expansion method is employed to construct the traveling wave solutions to the (3 + 1)-dimensional Kadomtsev–Petviashvili and (3 + 1)-dimensional nonlinear Schrödinger equations. Using suitable values of the parameters, the two- and three-dimensional figures of the obtained solutions are plotted. 

© 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: Sine-Gordon expansion method; Kadomtsev–Petviashvili equation; Schrödinger equation; wave solutions.