Lump periodic wave, soliton periodic wave, and breather periodic wave solutions for third-order (2+1)-dimensional equation

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.