Rogue waves on the periodic wave background in the Kadomtsev-Petviashvili I equation

Rogue waves arising on the background of two families of periodic standing waves in the Kadomtsev-Petviashvili I (KPI) equation are investigated. By the nonlinearization of spectral problem and Darboux transformation approach, the rogue wave solutions of the KPI equation on the Jacobian elliptic functions dn and cn background are derived. Darboux transformation is also used to introduce trigonometric function periodic background for the higher-order rogue wave in the KPI equation. On the plane wave background, some rogue waves, breathers and hybrid waves in the KPI equation are obtained as a byproduct in this paper. Moreover, the results represented in this paper enrich the dynamics of (2 + 1) dimensional nonlinear wave equations.