N-soliton, breathers, lumps and interaction solutions for a time-variable coefficients integrable equation in Kadomtsev-Petviashvili hierarchy

Considering the inhomogeneity of propagation media, the nonlinear integrable equations with variable coefficients have attracted much attention in recent years since they can model various physical phenomena in the real world more accurately. In this paper, a nonlinear integrable equation with time-variable coefficients in the Kadomtsev-Petviashvili hierarchy is investigated. By introducing specific variable transformation, the discussed equation is written into one differential equation with respect to the auxiliary function. This process is similar to the bilinearization in the Hirota bilinear method. Based on the perturbation approach, the N-soliton solutions are obtained, and the M-breather solutions are derived by imposing specific constraints on parameters. The lump solution is constructed by using the generalized positive quadratic function method. Besides, the long wave limit method is utilized to explore the T-lump solutions of this integrable equation. In addition, the 3D graphics of the solitons, breathers, lumps and their interaction are drawn to exhibit the physical properties of these solutions. These figures reflect that the time-variable coefficient leads to many novel dynamic behaviors, which are rather different from those for constant coefficient integrable equation. It should be pointed that the solution is the same as the general constant coefficients equations only in the case of the time-variable function as a constant. Therefore, the results obtained in this paper are more advantageous for the analysis of the complex physical applications governed by this model.