Bulletin of Computational Applied Mathematics (Bull CompAMa)
Solving the KPI wave equation with a moving adaptive FEM grid
The Kadomtsev-Petviashvili I (KPI) equation is the difficult nonlinear wave equation Uxt + 6Ux2 + 6UUxx + Uxxxx = 3Uyy. We solve this equation using PDE2D (www.pde2d.com) with initial conditions consisting of two lump solitons, which collide and reseparate. Since the solution has steep, moving, peaks, an adaptive finite element grid is used with a grading which moves with the peaks.
Keywords: KPI equation; adaptive finite element grid; nonlinear wave equation.