Breathers, lumps and hybrid solutions of the $(2{+}1)$-dimensional Hirota–Satsuma–Ito equation

Abstract

With the Hirota bilinear method and symbolic computation, explicit forms of $N$-soliton of the $\left(2+1\right)$-dimensional Hirota–Satsuma–Ito equation are derived. General high-order breather solutions are constructed through appropriate parameter restrictions. By performing an appropriate limiting procedures on soliton solutions and then making further parameter constraints, general lump solutions to the $\left(2+1\right)$-dimensional Hirota–Satsuma–Ito equation would be succinctly constructed. Furthermore, we provide the hybrid solutions which means different types of combinations in breathers, lumps and line solitons. In order to better understand the dynamical behaviors of the equation, the novel interaction and propagation characteristics are discussed graphically.