Geometrical patterns of time variable Kadomtsev-Petviashvili (I) equation that models dynamics of waves in thin films with high surface tension

Lump solutions are a prominent option for numerous models of nonlinear evolution. The intention of this research is to explore the variable coefficients Kadomtsev-Petviashvili equation. We auspiciously provide multiple soliton and M-lump solutions to this equation. Additionally, the presented results are also supplied with collision phenomena. Owing of its essential role, we employ appropriate parameter values to emphasis the physical characteristics of the provided results using 3D and contour charts. The outcomes of this work convey the physical characteristics of lump and lump interactions that occur in many dynamical regimes.

Automated summary

The purpose of this research is to investigate the variable coefficients Kadomtsev-Petviashvili equation, and successfully provide multiple soliton and M-lump solutions to this equation. The collision phenomena between these solutions are also studied. By employing appropriate parameter values, the physical characteristics of the results are emphasized using 3D and contour charts. The outcomes of this work reveal the physical characteristics of lump and lump interactions that occur in many dynamical regimes.