Abstract
This paper investigates the new periodic wave solutions for the third-order (2 + 1)-dimensional equation, which describes the wave propagation in shallow water, using the Hirota bilinear method and a three-wave method. The Lump Periodic wave, soliton periodic wave, and breather periodic have been represented by the three-dimensional images and contour images, by choosing the appropriate parameters, illustrating these solutions. The influence of the surface tension on the dynamics of the wave is also studied.
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