2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80153A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described by Hamilton-Jacobi type equations associated with hierarchies of dispersionless integrable systems. These hierarchies are constructed by applying the quasiclassical $\bar{\partial}$-dressing method.30 pages, tcilatexExactly Solvable and Integrable SystemsComplex Variablestext