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Hodograph‐Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations
Author(s) -
Kang Jing,
Qu Changzheng
Publication year - 2010
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/j.1467-9590.2009.00470.x
Subject(s) - hodograph , linearization , nonlinear system , mathematics , type (biology) , class (philosophy) , mathematical analysis , diffusion , point (geometry) , computer science , physics , geometry , ecology , quantum mechanics , artificial intelligence , biology , thermodynamics
In this paper, we study the problem of linearization of nonlinear systems of equationswhich is a potential form of systems of nonlinear diffusion equationsWe construct a class of point transformations of the formwhich connects the nonlinear systems with linear systems of equations . These point transformations are hodograph‐type transformations which have the property that the new independent and dependent variables depend, respectively, on the old dependent and independent variables. All systems of equations admitting such transformations are completely classified.