期刊
COMMUNICATIONS IN ANALYSIS AND GEOMETRY
卷 24, 期 3, 页码 605-643出版社
INT PRESS BOSTON, INC
DOI: 10.4310/CAG.2016.v24.n3.a7
关键词
evolution equations; nonlinear hyperbolic equations; pseudo-spherical surfaces; isometric immersions
类别
资金
- CRM-ISM post-doctoral Fellowship
- NSERC [RGPIN 105490-2011]
- Ministerio de Cithicia e Tecnologia, Brazil, CNPq [303774/2009-6]
We consider the class of differential equations that describe pseudo-spherical surfaces of the form u(t) = F(u, u(x), u(xx)) and u(xt) = F(u, u(x)). We answer the following question: Given a pseudo spherical surface determined by a solution a of such an equation, do the coefficients of the second fundamental form of the local isometric immersion in R-3 depend on a jet of finite order of u? We show that, except for the sine-Gordon equation, where the coefficients depend on a jet of order zero, for all other differential equations, whenever such an irrirrwrsion exists, the coefficients are universal functions of x and t, independent of u.
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