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Symbolic Representation and Classification of N = 1 Supersymmetric Evolutionary Equations
Author(s) -
Tian Kai,
Wang Jing Ping
Publication year - 2017
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/sapm.12163
Subject(s) - integrable system , scalar (mathematics) , mathematics , representation (politics) , the symbolic , pure mathematics , ring (chemistry) , algebra over a field , partial differential equation , mathematical analysis , geometry , psychology , chemistry , organic chemistry , politics , political science , psychoanalysis , law
We extend the symbolic representation to the ring of N = 1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Fréchet derivative, and super commutator, can be carried out in the symbolic way. Using the symbolic representation, we classify scalar λ‐homogeneous N = 1 supersymmetric evolutionary equations with nonzero linear term when λ > 0 for arbitrary order and give a comprehensive description of all such integrable equations.