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Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations
Author(s) -
Konopelchenko B.,
Alonso Martínez L.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00226
Subject(s) - integrable system , infinitesimal , nonlinear system , mathematics , plane (geometry) , mathematical analysis , dynamics (music) , class (philosophy) , type (biology) , classical mechanics , physics , geometry , quantum mechanics , computer science , ecology , artificial intelligence , acoustics , biology
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.