Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

Highlights: • Rogue solutions are proposed for Breaking Soliton equation from two quadratic polynomial. • A direct method is proposed to construct its rogue wave and one soliton and two solitons solutions. • The interactions between solitary waves and rogue waves are offered with a complete derivation. • Some 3D and contour plots are made to visualize the dynamics of higher dimensional nonlinear wave. - Abstract: Under inquisition in this paper is a $(2+1)$-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.