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Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations

B. Konopelchenko·L. Martinez Alonso
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Abstract

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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B. Konopelchenko, L. Martinez Alonso. 2002-01-21. Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations. https://arxiv.org/abs/nlin/0201039

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