New variable separation solutions for the generalized nonlinear diffusion equations

doi:10.1088/1674-1056/25/3/030202

中国物理B ›› 2016, Vol. 25 ›› Issue (3): 30202-030202.doi: 10.1088/1674-1056/25/3/030202

New variable separation solutions for the generalized nonlinear diffusion equations

Fei-Yu Ji(吉飞宇), Shun-Li Zhang(张顺利)

1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
2. Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China

收稿日期:2015-06-01 修回日期:2015-11-15 出版日期:2016-03-05 发布日期:2016-03-05
通讯作者: Fei-Yu Ji E-mail:feiyuji@xauat.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11371293, 11401458, and 11501438), the National Natural Science Foundation of China, Tian Yuan Special Foundation (Grant No. 11426169), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JQ1014).

New variable separation solutions for the generalized nonlinear diffusion equations

Fei-Yu Ji(吉飞宇)¹, Shun-Li Zhang(张顺利)²

1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
2. Center for Nonlinear Studies, School of Mathematics, Northwest University, Xi'an 710069, China

Received:2015-06-01 Revised:2015-11-15 Online:2016-03-05 Published:2016-03-05
Contact: Fei-Yu Ji E-mail:feiyuji@xauat.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11371293, 11401458, and 11501438), the National Natural Science Foundation of China, Tian Yuan Special Foundation (Grant No. 11426169), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JQ1014).

摘要/Abstract

摘要： The functionally generalized variable separation of the generalized nonlinear diffusion equations u_t=A(u,u_x)u_xx+ B(u,u_x) is studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie-Bäcklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.

关键词: conditional Lie-Bäcklund symmetry, functionally generalized separable solution, generalized nonlinear diffusion equation, invariant subspace

Abstract: The functionally generalized variable separation of the generalized nonlinear diffusion equations u_t=A(u,u_x)u_xx+ B(u,u_x) is studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie-Bäcklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided.

Key words: conditional Lie-Bäcklund symmetry, functionally generalized separable solution, generalized nonlinear diffusion equation, invariant subspace

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Sv (Lie algebras of Lie groups) 02.30.Ik (Integrable systems)

吉飞宇, 张顺利. New variable separation solutions for the generalized nonlinear diffusion equations[J]. 中国物理B, 2016, 25(3): 30202-030202.

Fei-Yu Ji(吉飞宇), Shun-Li Zhang(张顺利). New variable separation solutions for the generalized nonlinear diffusion equations[J]. Chin. Phys. B, 2016, 25(3): 30202-030202.

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New variable separation solutions for the generalized nonlinear diffusion equations

New variable separation solutions for the generalized nonlinear diffusion equations

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