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Pseudospherical Surfaces and Evolution Equations
Author(s) -
Chern S. S.,
Tenenblat K.
Publication year - 1986
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 - 10.1002/sapm198674155
Subject(s) - mathematics , mathematical analysis , surface (topology) , evolution equation , mathematical physics , geometry
We consider evolution equations, mainly of type u t = F ( u, u x ,..., ∂ k u/∂x k ), which describe pseudo‐spherical surfaces. We obtain a systematic procedure to determine a linear problem for which a given equation is the integrability condition. Moreover, we investigate how the geometrical properties of surfaces provide analytic information for such equations.