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The derivative-dependent functional variable separation for the evolution equations

Authors:	Zhang Shun-Li Lou Sen-Yue and Qu Chang-Zheng

Institution:	Institute of Modern Physics, Northwest University, Xi'an 710069, China; Department of Mathematics, Northwest University, Xi'an 710069, China; 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=Au,u_xu_xx+Bu,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.

Keywords:	derivative-dependent functional variable separation evolution equations generalized conditional symmetry
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