Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

Details Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

2002-01-21

arxiv.org/abs/nlin/0201039v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

30 pages, tcilatex

Scientific paper

A 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.

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