Nonisospectral Kadomtsev–Petviashvili equations from the Cauchy matrix approach

The Cauchy matrix approach is developed for solving nonisospectral Kadomtsev–Petviashvili equation and the nonisospectral modified Kadomtsev–Petviashvili equation. By means of a Sylvester equation $\boldsymbol{L}\boldsymbol{M}-\boldsymbol{M}\boldsymbol{K}=\boldsymbol{r}\boldsymbol{s}^{\mathrm T}$ , a set of scalar master functions $\{S^{(i,j)}\}$ are defined. We derive the evolution of scalar functions using the nonisospectral dispersion relations. Some explicit solutions are illustrated together with the analysis of their dynamics.