Solitons, breathers and rational solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation

This paper explores the Konopelchenko–Dubrovsky (KD) equation and employs Hirota’s bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique to construct solitons, line breathers, rational solutions, and algebraic solitons within the system. These solutions are represented using \(N \times N\) $N\times N$ determinants. When the determinant size N is odd, periodic background solutions are generated, while even N values yield solutions on constant backgrounds. By utilizing asymptotic analysis, the paper elucidates explicit expressions for asymptotic algebraic solitons localized in a straight line for the algebraic soliton solutions. The dynamics of the obtained solutions are further examined and illustrated through plots.