Nonlinear dynamics on the plane and integrable hierarchies of infinitesimal deformations
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2002
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Wiley-Blackwell
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Abstract
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.
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©2002 by the Massachusetts Institute of Technology.
The authors are very grateful to the Isaac Newton Institute for Mathematical Sciences of Cambridge, where this work has been done and written, for the kind hospitality. They are also grateful to the organizers of the programme “Integrable Systems” for the support provided. L. Martínez Alonso wishes to thank the Fundacion Banco Bilbao Vizcaya Argentaria for supporting his stay at Cambridge University as a BBV visiting professor.