Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions

A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Special cases include the integrable KP (Kadomtsev-Petviashvili) its modified version, as well their generalizations. Two main results are obtained. First, all low-order conservation laws derived, including ones that arise for special powers p. The comprise momenta, energy, Galilean-type quantities, topological charges. Their physical meaning properties discussed. charges shown to give rise integral constraints on initial data Cauchy problem. Second, line-soliton solutions obtained an explicit form. parameterization given using speed direction angle of line-soliton, allowed kinematic region determined terms these parameters. Basic kinematical line-solitons also These differ significantly compared those line-shock solution emerge when a limiting case considered.