Abstract
This article secures the new exact wave structures to Dullin-Gottwald-Holm (DGH) equation which is used as a governing model to explain the behaviour of waves in shallow water. The wave structures in the forms of solitary, shock, singular, shock-singular as well as hyperbolic, singular periodic and rational solutions are secured with the aid of computational strategy namely modified direct algebraic and ansatz approaches. The constraint conditions which ensure the validity of new wave structures are also reported. Moreover, the graphs of the solution attained are recorded in terms of 3D, 2D and contour plots by fixing parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.
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