Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

A class of nonlinear problems on the plane, described by nonlinear inhomogeneous ‐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 ‐dressing method.