LAUSR

The primary attention of this work focuses on finding rational and generalized rational solutions for the (2 + 1)-dimensional Kadomtsev–Petviashvili equation that can be used to describe nondispersive and nondiffractive localized wave packet in power law nonlinear media. Specifically, the (2 + 1)-dimensional nonlinear Schrödinger equation with power law nonlinearity is first transformed into the Kadomtsev–Petviashvili equation. Then, through the bilinear form and symbolic computation, we derive two hierarchies of multi-lump solitary waves, composing of three, six, and eight lump waves. The obtained solutions observe a specific ‘circularity structure’ that the lump waves sit at the same circular. In addition, we illustrate that these waves are stable during propagation.