Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation

Mats Ehrnström, Mark Groves

The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(β-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tens…