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WTC Expansions and Nonintegrable Equations[Note 1. Presented at the Conference on Nonlinear Equations, January 1997, ...]
Author(s) -
Kichenassamy S.
Publication year - 1999
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 - 10.1111/1467-9590.00102
Subject(s) - gravitational singularity , mathematics , generalization , ode , reduction (mathematics) , nonlinear system , representation (politics) , mathematical analysis , class (philosophy) , geometry , physics , law , quantum mechanics , artificial intelligence , politics , political science , computer science
This article presents a generalization, to nonintegrable equations, of the ARS‐WTC method for the generation of singular solutions of PDE and ODE. The argument rests on the reduction of the equation to a generalized nonlinear Fuchsian equation and automatically ensures a representation of singularities by convergent expansions. Practical issues in the reduction process are emphasized. Finally, it is shown that a class of unstable characteristic singularities is related to the degeneration of noncharacteristic singularities.