Classification of Bäcklund transformations for second-ordor nonlinear PDES(一类二阶非线性偏微分方程Bäecklund变换的分类)
讨论形如ut = F(u，ux, uxx)的非线性偏微分方程由可积系统vx = P(v，u，ux），vt = Q(v，u，ux）定义的Bäcklund变换u ↦ v分类问题，证明了这样的非线性偏微分方程只能是Burgers方程ut = uxx + 2uux，而相应的可积系统是vx = (λ+v)(u-v)，vt = (λ +v）（u2+ux — uv）—λ(λ + v)（u — v），其中λ是任意常数....
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2011-01-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
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| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2011.01.005 |