Abstract
This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.
Highlights
This century, soliton theory has been one of the most important theories of nonlinear sciences.Mathematically, one of such fields where this theory has been considered has the aim of explaining the propagation of water waves
One of such fields where this theory has been considered has the aim of explaining the propagation of water waves
Such wave propagation has been observed in quantum mechanics, electricity, optical soliton, optical fibers, viscoelasticity, mathematics, physics, chemistry and in many other areas
Summary
This century, soliton theory has been one of the most important theories of nonlinear sciences. A modified version of this method was introduced in [34] to extend the Hirota bilinear form of the Boussinesq equation which had been derived in [30] This model describes the propagation of shallow water waves within the small amplitudes as they propagate at a uniform speed in a water canal of constant depth. We underline the novelty of these results via a conclusion section
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