Nonisospectral Kadomtsev–Petviashvili equations from the Cauchy matrix approach

Abstract

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.