中国物理B ›› 2006, Vol. 15 ›› Issue (12): 2765-2776.doi: 10.1088/1009-1963/15/12/001

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The derivative-dependent functional variable separation for the evolution equations

楼森岳1, 屈长征2, 张顺利3   

  1. (1)Center of Nonlinear Science, Ningbo University, Ningbo 315211, China; (2)Department of Mathematics, Northwest University, Xi'an 710069, China; (3)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
  • 收稿日期:2005-09-24 修回日期:2005-11-09 出版日期:2006-12-20 发布日期:2006-12-20
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2005-09-24 Revised:2005-11-09 Online:2006-12-20 Published:2006-12-20
  • Supported by:
    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).

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摘要： This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt=Au,uxuxx+Bu,ux,ut which admits the derivative-dependent functional separable solutions DDFSSs). We also extend the concept of the DDFSS to cover other variable separation approaches.

关键词: derivative-dependent functional variable separation, evolution equations, generalized conditional symmetry

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.

Key words: derivative-dependent functional variable separation, evolution equations, generalized conditional symmetry

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Ik (Integrable systems)