Dynamics of the breathers, rogue waves and solitary waves in the (2+1)-dimensional Ito equation

In this paper, the homoclinic breather limit method is employed to find the breather wave and the rational rogue wave solutions of the (2+1)-dimensional Ito equation. Moreover, based on its bilinear form, the solitary wave solutions of the equation are also presented with a detailed derivation. The dynamic behaviors of breather waves, rogue waves and solitary waves are analyzed with some graphics, respectively. The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the (2+1)-dimensional Ito equation.