Evolution of lump solutions for the KP equation

摘要: Abstract The two (space)-dimensional generalisation of the Korteweg-de Vries (KdV) equation is Kadomtsev-Petviashvili (KP) equation. This possesses solitary wave type solutions. One independent direction orthogonal to propagation and soliton solution KdV extended space dimensions. other a true two-dimensional which decays zero in all directions. It this second considered present work. known that KP admits an inverse scattering solution. However only applies for initial conditions decay at infinity faster than reciprocal distance from origin. To study evolution lump-like condition, group velocity argument used determine linear dispersive radiation generated as lump evolves. Using information combined with conservation equations suitable trial function, approximate ODEs governing isolated pulse are derived. These solutions have similar form equation, but varying parameters. found asymptotically stable, depending on conditions, either lower amplitude (shedding mass) or narrows down higher amplitude. compared full numerical good agreement found.