New variable separation approach: Application to nonlinear diffusion equations

Journal of Physics A: Mathematical and General

Volumn 36, Issue 49, 2003, Pages 12223-12242

  Zhang, Shun Li ^a,b   Lou, S Y ^a,c   Qu, Chang Zheng ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b NORTHWEST UNIVERSITY   (China)

^c NINGBO UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347622670     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/49/006     Document Type: Article

References (100)

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2. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
3. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
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6. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
7. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
8. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
9. Olver P J 1993 Application of Lie Groups to Differential Equation (Graduate Texts Math. vol 107) 2nd edn (New York: Springer) Ames W F 1972 Nonlinear Partial Differential Equations in Engineering vol II (New York: Academic) Bluman G W and Kumei S 1989 Symmetries and Differential Equation (Appl. Math. Sci. vol 81) (Berlin: Springer) Dorodnitsyn V A 1982 USSR Comput. Math. Phys. 22 115 Hill J M, Avagliano A J and Edwards M P 1992 IMA J. Appl. Math. 48 283 Frey H D, Glöckle W G and Nonnenmacher T T 1993 J. Phys. A: Math. Gen. 26 665 Cherniha R M and Serov M I 1998 Eur. J. Appl. Math. 9 527 Galaktionov V A, Dorodnitsyn V A, Elenin G G, Kurdyumov S P and Samarskii A. A 1988 J. Sov. Math. 41 1222 Lou S Y 2000 J. Math. Phys. 41 6509
10. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
11. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
12. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
13. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
14. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
15. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
16. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
17. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
18. Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025 Fushchich W I, Shtelen W M and Serov N I 1993 Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Dordrecht: Kluwer) Clarkson P A and Mansfield E L 1993 Physica D 70 250 Nucci M C and Clarkson P A 1992 Phys. Lett. A 164 4 Nucci M C 1993 J. Math. Anal. Appl. 178 294 Nucci M C 1994 Physica D 78 124 Estevez P G 1994 J. Phys. A: Math. Gen. 27 2113 Arrigo D J, Broadbridge P and Hill J M 1994 IMA J. Appl. Math. 52 1 Pucci E 1992 J. Phys. A: Math. Gen. 25 2631
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45. Newell A C, Tabor M and Zeng Y B 1987 Physica D 29 1 Cariello F and Tabor M 1989 Physica D 39 77 Estevez P G and Gordoa P R 1990 J. Phys. A: Math. Gen. 23 4831 Pickering A 1993 J. Phys. A: Math. Gen. 26 4395 Musette M and Conte R 1994 J. Phys. A: Math. Gen. 27 3895 Musette M, Conte R and Pickering A 1995 J. Phys. A: Math. Gen. 28 179 Pickering A 1996 J. Math. Phys. 37 1894 Lou S Y 1998 Z. Naturforsch. A 53 251 Chen C L, Tang X Y and Lou S Y 2002 Phys. Rev. E 66 6605
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