A (2 + 1)-dimensional breaking soliton equation associated with the Kaup–Newell soliton hierarchy

A new (2 + 1)-dimensional breaking soliton equation is constructed and its zero curvature representation is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy provide with a solution of the new breaking soliton equation. With the help of the Darboux transformation of the Kaup–Newell soliton hierarchy, an explicit solution of the new equation is obtained.