Abstract
In this paper, two solitary wave solutions are obtained for the Vakhnenko–Parkes equation with power law nonlinearity by the ansatz method. Both topological as well as non-topological solitary wave solutions are obtained. The parameter regimes, for the existence of solitary waves, are identified during the derivation of the solution.
Highlights
The theory of nonlinear evolution equations (NLEEs) is an important area of research in the area of applied mathematics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
A challenging task is to look for solutions of these NLEEs
The importance of the results presented here is two-fold
Summary
The theory of nonlinear evolution equations (NLEEs) is an important area of research in the area of applied mathematics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. A challenging task is to look for solutions of these NLEEs. There are various types of solutions that are available for these equations. Some of them are soliton solutions, solitary wave solutions, cnoidal and snoidal waves, periodic solutions, shock wave solutions as well as various other types. In this paper there will be one such NLEE that will be studied. This is the Vakhnenko–Parkes (VP) equation with power law nonlinearity. The ansatz method will be used to retrieve the topological as well as non-topological solitary wave solution. The domain restrictions will be revealed during the process of obtaining the solutions
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