Abstract
In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.
Highlights
During the past years, soliton solutions are considerably important issue in biophysics, geophysical sciences, chemical kinematics, optical fibers, technology of space, electricity, elastic media and several topics in nonlinear sciences.In recent years, most authors have presented several methods to find the soliton solutions of NLEEs such as (G’/G)-expansion method [1], exp-function method [2], the tanh method [3] and many more
If we compare the exact solutions of Eq (1) and Eq (2) reported by the other authors, our solution (17) is a similar solution with the solution (4.15) in [7]
We can conclude that this method has a significiant role in observing NLEEs and it is highly strong with regard to yielding analytical solutions of NLEEs
Summary
Soliton solutions are considerably important issue in biophysics, geophysical sciences, chemical kinematics, optical fibers, technology of space, electricity, elastic media and several topics in nonlinear sciences. GKM [4] will be used to find exact solutions of (1+1) dimensional nonlinear Ostrovsky equation. Eq (1) is a model for weakly nonlinear surface and internal waves in a rotating ocean This equation has been introduced by Vakhnenko and Parkers [5]. Some authors have used various methods to find travelling wave solutions of this equation [7,8,9,10,11]. This equation has been obtained by Fokas by expanding the Lax pairs of the integrable.
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