Grammian Solutions to a Non-Isospectral Kadomtsev--Petviashvili Equation

Solutions in the Grammian form for a non-isospectral Kadomtsev--Petviashvili equation are derived by means of Pfaffian derivative formulae. Explicit entries of the Grammian are given. Non-isospectral dynamics of the solutions generated from the Grammian are investigated in an analytic way. The solutions obtained can describe line solitons in non-uniform media travelling with time-dependent amplitude and time-dependent direction. In addition, some other solutions have singularities.