Rational solutions of the (2+1)-dimensional Kaup–Kupershmidt equation

Abstract Rational solutions of the (2+1)-dimensional Kaup–Kupershmidt equation are presented in determinant form by taking the long wave limit of soliton solutions. With the appropriate parameters’ form, the soliton solution is firstly changed into the mixed solution consisting of solitons and periodic waves. Then taking the limit of the fixed parameter gives rise to the rational solution, which represents the interaction between the rational line soliton and the lump. It is shown that the rational line soliton exhibits the W-shaped soliton, while the lump is classified into the double-peak and the single-peak patterns. The interactions between two types of rational waves are discussed in different cases.