Variable separation and exact solutions to generalized nonlinear diffusion equations

Chinese Physics Letters

Volumn 19, Issue 12, 2002, Pages 1741-1744

  Zhang, Shun Li ^a,b   Lou, Sen Yue ^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

PARTIAL DIFFERENTIAL EQUATIONS;

CANONICAL FORM; EXACT SOLUTION; NONLINEAR DIFFUSION EQUATIONS; VARIABLE SEPARATION APPROACH; VARIABLE SEPARATION SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 0036904459     PISSN: 0256307X     EISSN: None     Source Type: Journal    
DOI: 10.1088/0256-307X/19/12/301     Document Type: Article

References (47)

1. Olver P.J. 1993 Application of Lie Groups to Differential Equation 2nd edn, Graduate Texts Math. 107 (New York: Springer).
2. Lou S.Y. 2000 J. Math. Phys. 41 6509.
3. Bluman G.W. and Cole J.D. 1969 J. Math. Mech. 18 1025.
4. Clarkson P.A. and Mansfield E.L. 1993 Physics D 70 250.
5. Clarkson P.A. and M.D. Kruskal 1989 J. Math. Phys. 39 2201.
6. Lou S.Y. 1990 Phys. Lett. A 151 133.
7. Clarkson P.A. 1995 Chaos Solitons Fractals 5 2261.
8. Lou S.Y. Ruan H.Y. Chen D.F. and Chen W.Z. 1991 J. Phys. A: Math. Gen. 24 1455.
9. Lou S.Y. 1990 J. Phys. A: Math. Gen. 23 L649.
10. Pucci E. 1993 J. Phys. A: Math. Gen. 26 681.
11. Saccomandi G. 1997 J. Phys. A: Math. Gen. 30 2211.
12. Lou S.Y. Tang X.Y. and Lin J 2000 J. Math. Phys. 41 8286.
13. Lou S.Y. and Tang X.Y. 2001 Chin. Phys. 10 897.
14. Tang X.Y. and Lou S.Y. 2002 Chin. Phys. Lett. 19 1.
15. Lou S.Y. 2000 Chin. Phys. Lett. 17 781.
16. Fokas A.S. and Lin Q.M. 1994 Phys. Rev. Lett. 72 3293.
17. Zhdanov R.Z. 1995 J. Phys. A: Math. Gen. 28 3841.
18. Qu C.Z. 1997 Stud. Appl. Math. 99 107.
19. Qu C.Z. 1999 IMA J. Appl. Math. 62 283.
20. Qu C.Z. 2000 Nonlinear Anal. Theory. Meth. Appl. 42 301.
21. Bluman G.W. Reid J D. and Kumei S. 1988 J. Math. Phys. 29 806.
22. Lou S.Y. 1996 Phys. Scr. 54 428.
23. Lou S.Y. 1994 J. Nonlinear Math. Phys. 1 401.
24. Lou S.Y., Ruan H.Y., Chen W.Z., Wang Z.L. and Chen L.L. 1994 Chin. Phys. Lett. 11 593.
25. Musette M. Conte R. and Piekering A. 1995 J. Phys. A: Math. Gen. 28 179.
26. Bickering A. 1996 J. Math. Phys. 37 1894.
27. Lou S.Y. 1998 Z. Naturf. A 53 251.
28. Chert C.L., Tang X.Y. and Lou S.Y. 2002 Phys. Rev. E 66 036605.
29. Tang X.Y. and Hu H.C. 2002 Chin. Phys. Lett. 19 1225.
30. Galaktionov V.A. 1994 Nonlinear Anal. Theory. Meth. & Appl. 23 1595.
31. Svirshchevskii S.R. 1995 Phys. Lett. A 199 344.
32. King J.R. 1990 J. Phys. A: Math. Gen. 23 3681.
33. Estevez P.G. 1992 Phys. Lett. A 171 259.
34. Cherniha R.M. 1998 J. Phys. A: Math. Gen. 31 8179.
35. Pucci E. and Saccomandi G. 2000 Physica D 139 28.
36. Qu C.Z. Zhang S.L. and Liu R.C. 2000 Physica D 144 97.
37. Estevez P.G. Qu C.Z. and Zhang S.L. 2002 J. Math. Anal. Appl. (at press).
38. Zhang S.L. Lou S.Y. and Qu C.Z. 2002 Physica D (submitted).
39. Miller W. 1977 Symmetry and Separation of Variables (Reading, MA: Addison-Wesley).
40. Kalnins E.G. Miller W. 1985 J. Math. Phys. 26 2168.
41. Zhdanov R.Z. 1997 J. Math. Phys. 38 1197.
42. Dolye P.W. Vassiliou P.J. 1998 Int. J. Nonlinear Mech. 33 315.
43. Cao C.W. 1990 Sci. Chin. A 33 528.
44. Lou S.Y., Tang X.Y. and Chen C.L. 2002 Chin. Phys. Lett. 19 769.
45. Tang X.Y. and Lou S.Y. 2002 Chaos Solitons Fractals 14 2451.
46. Lin J. 2002 Chin. Phys. Lett. 19 765.
47. Tang X.Y., Lou S.Y. and Zhang Y. 2002 Phys. Rev. E (at press).