The derivative-dependent functional variable separation for the evolution equations
Zhang Shun-Li(张顺利)a)b)c)†, Lou Sen-Yue(楼森岳)c), and Qu Chang-Zheng(屈长征)b)
a Institute of Modern Physics, Northwest University, Xi'an 710069, China; b Department of Mathematics, Northwest University, Xi'an 710069, China; c Center of Nonlinear Science, Ningbo University, Ningbo 315211, China
Abstract This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation $u_{tt}=A(u, u_x)u_{xx}+B(u,u_x, u_t)$ which admits the derivative-dependent functional separable solutions DDFSSs). We also extend the concept of the DDFSS to cover other variable separation approaches.
Received: 24 September 2005
Revised: 09 November 2005
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China Grant Nos 10371098, 10447007
and 10475055), the Natural
Science Foundation of Shaanxi Province of China Grant No 2005A13).
Cite this article:
Zhang Shun-Li(张顺利), Lou Sen-Yue(楼森岳), and Qu Chang-Zheng(屈长征) The derivative-dependent functional variable separation for the evolution equations 2006 Chinese Physics 15 2765
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