Rogue wave for the ()-dimensional Kadomtsev–Petviashvili equation

In this work, a new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. ( 2 + 1 )-dimensional Kadomtsev–Petviashvili equation is used as an example to illustrate the effectiveness of the suggested method. A new family of two-wave solution, rational breather wave solution, is obtained by extended homoclinic test method, and it is just a rogue wave solution. This result shows rogue wave can come from extreme behavior of breather solitary wave for ( 2 + 1 )-dimensional nonlinear wave fields.