Exact solutions for the transformed reduced Ostrovsky equation via the [formula omitted]-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions

Abstract

Although the F-expansion method is a relatively old method for obtaining exact solutions for nonlinear partial differential equations, its advantage over the other auxiliary equation methods is shown in this work for solving the transformed reduced Ostrovsky equation. In fact, to the authors’ knowledge, this is the first time that a largest number of exact solutions for the auxiliary equation F′(ω)=PF4(ω)+QF2(ω)+R has been presented. It is used in this work to get 52 types of exact solution: six for Weierstrass-elliptic function solutions and the rest for Jacobian-elliptic function solutions. However, in consideration of Parkes (2010) [9], who states that the term ‘new’ has to be used very carefully, it is very important to mention that the solutions obtained are not completely different. Many examples for proving Parkes’s view [9] have been examined. Moreover, soliton-like solutions and trigonometric-function solutions are also obtained as limiting cases. The previous results determined by the hyperbolic tangent method (Yusufoğlu and Bekir, 2007) [5] and exponential function approach (Kangalgil and Ayaz, 2008) [6] are found to be limited and special cases of the current results.