https://doi.org/10.1140/epjp/i2018-12085-y
Regular Article
Solitons in an inhomogeneous Murnaghan’s rod
1
University of Tuscia, Engineering School (DEIM), 01100, Viterbo, Italy
2
Firat University, Faculty of Science, 23119, Elazig, Turkey
3
Federal University Dutse, Faculty of Science, 23119, Dutse, Jigawa, Nigeria
4
Munzur University, Faculty of Engineering, 63100, Tunceli, Turkey
5
Final International University, Faculty of Education, Kyrenia, Cyprus
* e-mail: hbulut@firat.edu.tr
Received:
4
April
2018
Accepted:
7
May
2018
Published online:
19
June
2018
In this paper, we construct a family of wave solutions to the doubly dispersive equation, such as topological, non-topological, singular, compound topological-non-topological bell-type and compound singular, soliton-like, singular periodic wave and exponential function solutions. These analytical solutions are obtained by using the extended sinh-Gordon equation expansion method and the modified 
-expansion function method. The doubly dispersive equation is an important nonlinear physical model describing the nonlinear wave propagation in the elastic inhomogeneous Murnaghan’s rod. Under a suitable choice of parameters, the 2D, 3D and contour graphics to the reported results are also plotted.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
