New variable separation solutions for the generalized nonlinear diffusion equations

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

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.

Keywords: conditional Lie-Bäcklund symmetry functionally generalized separable solution generalized nonlinear diffusion equation invariant subspace

Received: 01 June 2015
Revised: 15 November 2015
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.20.Sv	(Lie algebras of Lie groups)
	02.30.Ik	(Integrable systems)

Fund: 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).

Corresponding Authors: Fei-Yu Ji
E-mail: feiyuji@xauat.edu.cn

Cite this article:

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

[1]	Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Springer-Verlag)
[2]	Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer-Verlag)
[3]	Ibragimov N H 1985 Transformation Groups Applied to Mathematical Physics (Boston: Reidel)
[4]	Ovsiannikov L V 1982 Group Analysis of Differential Equations (New York: Academic Press)
[5]	Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025
[6]	Ames W F 1972 Nonlinear Partial Differential Equations in Engineering (New York: Academic Press)
[7]	Levi D and Winternitz P 1989 J. Phys. A: Math. Gen. 22 2915
[8]	Wang J Y, Tang X Y, Liang Z F and Lou S Y 2015 Chin. Phys. B 24 050202
[9]	Hu X R and Chen Y 2015 Chin. Phys. B 24 090203
[10]	Liu X Z, Yu J and R B 2015 Chin. Phys. B 24 030202
[11]	Wang X, Ma T B and Ning J G 2014 Chin. Phys. Lett. 31 030201
[12]	Yi L N and Taogetusang 2015 Acta Phys. Sin. 64 020201 (in Chinese)
[13]	CLarkson P A and Kruskal M D 1989 J. Math. Phys. 30 2201
[14]	Lou S Y 1990 Phys. Lett. A 151 133
[15]	Fuschch W I and Zhdanov R Z 1994 J. Nonlinear Math. Phys. 1 60
[16]	King J R 1993 Physica D 64 35
[17]	Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283
[18]	Fokas A S and Liu Q M 1994 Phys. Rev. Lett. 72 3293
[19]	Zhdanov R Z 1995 J. Phys. A: Math. Gen. 128 3841
[20]	Qu C Z, Zhang S L and Liu R C 2000 Physica D 144 97
[21]	Feng W and Ji L N 2013 Physica A 392 618
[22]	Zhang S L, Lou S Y and Qu C Z 2003 J. Phys. A: Math. Gen. 36 12223
[23]	Di Y M, Zhang D D, Shen S F and Zhang J 2014 Appl. Math. Model. 38 4409
[24]	Zhang S L, Lou S Y and Qu C Z 2002 Chin. Phys. Lett. 19 1741
[25]	Ji F Y and Yang C X 2013 Chin. Phys. B 22 100202
[26]	Galaktionov V A and Svirshchevskii S R 2007 Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics (London: Chapman and Hall/CRC)

[1]	Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension Qu Gai-Zhu (屈改珠), Zhang Shun-Li (张顺利), Li Yao-Long (李尧龙). Chin. Phys. B, 2014, 23(11): 110202.
[2]	Second-order nonlinear differential operators possessing invariant subspaces of submaximal dimension Zhu Chun-Rong(朱春蓉). Chin. Phys. B, 2011, 20(1): 010201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New variable separation solutions for the generalized nonlinear diffusion equations

Cite this article:

Online attention