The second Painlevé equation as a model for the electric field in a semiconductor

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

Volumn 233, Issue 4-6, 1997, Pages 397-400

  Kudryashov, Nicolai A ^a  

^a NATIONAL RESEARCH NUCLEAR UNIVERSITY MEPHI   (Russian Federation)

Author keywords

Electric field; Painlev property; Second Painlev equation; Semiconductor

Indexed keywords

SEMICONDUCTOR MATERIALS;

PAINLEVE; SPECIAL SOLUTIONS;

ELECTRIC FIELDS;

EID: 0008117890     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(97)00545-8     Document Type: Article

References (20)

1. M.J. Ablowitz and P.A. Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge Univ. Press, Cambridge, 1994).
2. R. Conte, Singularities of differential equations and integrability, in: An Introduction to Methods of Complex Analysis and Geometry for Classical Mechanics and Nonlinear Waves, eds. D. Denest and C. Froeshle (Editions Frontiéres, Gif-sur-Yvette, 1994) p. 49.
3. M.J. Ablowitz and H. Segur, Phys. Rev. Lett. 38 (1977) 1103.
4. M.J. Ablowitz, A. Ramani and H. Segur, Lett. Nuov. Cimento 23 (1978) 333.
5. M.J. Ablowitz, A. Ramani and H. Segur, J. Math. Phys. 21 (1980) 715; 21 (1980) 1006.
6. M.J. Ablowitz, A. Ramani and H. Segur, J. Math. Phys. 21 (1980) 715; 21 (1980) 1006.
7. J. Weiss, M. Tabor and G. Carnevale, J. Math. Phys. 24 (1983) 522.
8. J. Weiss, Solitons in Physics, Mathematics and Nonlinear Optics, eds. P.J. Olver and D.H. Sattinger (Springer, Berlin, 1990) p. 175.
9. N.A. Kudryashov, S.S. Kucherenko and Yu. I Sitsko, Math. Simul. 1 (1989) 12 [in Russian].
10. N.A. Kudryashov and S.S. Kucherenko Physics and Technics of Semiconductors 25 (1991) 1188 [in Russian].
11. S.S. Kucherenko and N.A Kudryashov, Solid-State Elec., 35 (1992) 993.
12. A.P. Krishchenko, Phys. Lett. A 203 (1995) 350.
13. V.I. Gromak, Diff. Eqs. 18 (1982) 753 [in Russian].
14. E. Gambier, Acta Math. 33 (1910) 1.
15. M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM Philadelphia, 1981).
16. N.A. Lukashevich, Diff. Eqs. 6 (1972) 1124 [in Russian].
17. H. Airault, Stud. Appl. Math. 61 (1979) 33.
18. M. Boiti and E. Pempinelli, Nuovo Cimento 51 B (1979) 70.
19. A.S. Kompaneets, Physical, chemical and relativistic hydrodynamics (Nauka, Moscow, 1977) [in Russian].
20. L.E. Kalichman, Elements of magnetic hydrodynamics (Atom Publishing House, Moscow, 1964) [in Russian].