Exact solutions for a diffusion equation with a nonlinear external force

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 372, Issue 14, 2008, Pages 2359-2363

  Zola, R S ^a   Lenzi, M K ^b   Evangelista, L R ^a   Lenzi, E K ^a   Lucena, L S ^c   da Silva, L R ^c  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^c FEDERAL UNIVERSITY OF RIO GRANDE DO NORTE   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EXPONENTIAL FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFUSION EQUATIONS; EXACT SOLUTION; EXTERNAL FORCE; ONE-DIMENSIONAL DIFFUSION EQUATIONS; STATIONARY SOLUTIONS; TIME DEPENDENT; TSALLIS FORMALISM;

NONLINEAR EQUATIONS;

EID: 40249098161     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.12.007     Document Type: Article

References (51)

1. W.A. Woyczynski Burgers-KPZ Turbulence: Gottingen Lectures Lecture Notes in Mathematics 1999 Springer-Verlag Telos
2. U. Frish J. Bec Burgulence M. Lesieur F. David A.M. Yaglom Proceedings of the Les Houches Summer School, 2000, New Trends in Turbulence 2001 Springer EDP-Sciences Berlin
3. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Singapore
4. R. Metzler J. Klafter Phys. Rep. 339 2000 1
5. L. Debnath Nonlinear Partial Differential Equations for Scientists and Engineers 1997 Birkhäuser Boston
6. J.D. Logan An Introduction to Nonlinear Partial Differential Equations 1994 John Wiley New York
7. T.D. Frank Nonlinear Fokker–Planck Equations 2005 Springer-Verlag Heidelberg
8. B.J. West M. Bologna P. Grigolini Physics of Fractal Operators 2002 Springer-Verlag New York
9. G.M. Zaslavsky Phys. Rep. 371 2002 461
10. J. Bec Phys. Rev. Lett. 87 2001 104501
11. J. Stephenson Physica A 222 1995 234
12. H. Spohn J. Phys. I France 3 1993 69
13. D.S.F. Crothers D. Holland Y.P. Kalmykov W.T. Coffey J. Mol. Liq. 114 2004 27
14. J.F. Douglas, in Ref. [3] , pp. 241–331
15. H. Schiessel, Ch. Friedrich, A. Blumen, in Ref. [3] , pp. 331–376
16. H. Schriessel A. Blumen Fractals 3 1995 483
17. R. Metzler E. Barkai J. Klafter Physica A 266 1999 343
18. P. Olesen Phys. Rev. E 68 2003 016307
19. A. Iomin Phys. Rev. E 73 2006 061918
20. C. Tsallis D.J. Bukman Phys. Rev. E 54 1996 R2197
21. J.M. Burgers The Nonlinear Diffusion Equation 1974 Reidel Holland
22. L. Borland F. Pennini A.R. Plastino A. Plastino Eur. Phys. J. B 12 1999 285
23. P.C. Assis Jr. P.C. da Silva L.R. da Silva E.K. Lenzi M.K. Lenzi J. Math. Phys. 47 2006 103302
24. G. Drazer H.S. Wio C. Tsallis Phys. Rev. E 61 2000 1417
25. A. Rigo A.R. Plastino M. Casas Phys. Lett. A 276 2000 97
26. A.R. Plastino M. Casas A. Plastino Physica A 280 2000 289
27. M. Bologna C. Tsallis P. Grigolini Phys. Rev. E 62 2000 2213
28. C. Tsallis E.K. Lenzi Chem. Phys. 284 2002 341
29. C. Tsallis E.K. Lenzi Chem. Phys. 287 2002 295 Erratum
30. E.K. Lenzi R.S. Mendes K.S. Fa L.S. Moraes L.R. da Silva L.S. Lucena J. Math. Phys. 46 2005 83506
31. S.R.A. Salinas C. Tsallis Braz. J. Phys. 29 1 1999
32. S. Abe Y. Okamoto Nonextensive Statistical Mechanics and Its Applications Lecture Notes in Physics 2001 Springer-Verlag Heidelberg
33. P. Grigolini C. Tsallis B.J. West Chaos Solitons Fractals 13 3 2002
34. A.R. Plastino A. Plastino Physica A 222 1995 347
35. D. Mitra J. Bec R. Pandit U. Frisch Phys. Rev. Lett. 94 2005 194501
36. E. Moreau O. Vallée Phys. Rev. E 73 2006 016112
37. P. Garbaczewski Phys. Rev. E 74 2006 028101
38. E. Moreau O. Vallée Phys. Rev. E 74 2006 028102
39. S.V. Petrovskii Zh. Tekh. Fiz. 69 1999 10
40. S. Eule R. Friedrich Phys. Lett. A 351 2006 238
41. R.S. Zola, J.C. Dias, E.K. Lenzi, L.R. Evangelista, M.K. Lenzi, L.R. da Silva, preprint, 2007
42. C. Sphocleous Chaos Solitons Fractals 20 2004 1047
43. W.P. Hong Phys. Lett. A 268 2000 81
44. P. Garbaczewski G. Kondrat R. Olkiewicz Chaos Solitons Fractals 9 1998 29
45. P. Garbaczewski G. Kondrat R. Olkiewicz Phys. Rev. E 55 1997 1401
46. P. Broadbridge J. Eng. Math. 36 2004 25
47. H. Risken The Fokker–Planck Equation 1984 Springer-Verlag New York
48. C.W. Gardiner Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences Springer Series in Synergetics 1996 Springer-Verlag New York
49. M.O. Vlad Chaos Solitons Fractals 4 1994 191
50. M.P. Morse H. Feshbach Methods of Theoretical Physics 1953 McGraw–Hill New York
51. G.B. Whitham Linear and Nonlinear Waves 1974 John Wiley New York