|
|
|
|
Список литературы
|
|
| |
| 1. |
F. J. Bureau, “Integration of some nonlinear systems of ordinary differential equations”, Ann. Mat. Pura Appl. (4), 94 (1972), 345–359 |
| 2. |
F. J. Bureau, “Sur des systèmes différentiels du troisième ordre et les
équations différentielles associées”, Acad. Roy. Belg. Bull. Cl. Sci. (5), 73:6–9 (1987), 335–353 |
| 3. |
F. Calogero, W. Eckhaus, “Nonlinear evolution equations, rescalings, model PDEs and their
integrability. I”, Inverse problems, 3 (1987), 229–262 |
| 4. |
F. Calogero, S. de Lillo, “The Eckhaus PDE $i\psi_t + \psi_{xx} + 2(\vert\psi\vert^2)_x\psi +
\vert\psi\vert^4\psi = 0$”, Inverse Problems, 4:2 (1988), 571 |
| 5. |
J. Chazy, “Sur les équations différentielles du troisième ordre et d'ordre
supérieur dont I'intégrale générale a ses points critiques fixes”, Acta Math., 34:1 (1911), 317–385 |
| 6. |
P. A. Clarkson, “Dimensional reductions and exact solutions of a generalized nonlinear
Schrödinger equation”, Nonlinearity, 5 (1992), 453–472 |
| 7. |
P. A. Clarkson, C. M. Cosgrove, “The Painlevé property and a generalised derivative nonlinear
Schrödinger equation”, J. Phys. A, 20 (1987), 2003–2024 |
| 8. |
R. Conte, “Invariant Painlevé analysis of partial differential equations”, Phys. Lett. A, 140 (1989), 383–390 |
| 9. |
R. Conte, “Unification of PDE and ODE versions of Painlevé analysis into a
single invariant version”, Painleve transcendents, their asymptotics and physical applications, eds. D. Levi, P. Winternitz, Plenum, New York, 1992, 125–144 |
| 10. |
R. Conte, A. P. Fordy, A. Pickering, “A perturbative Painleve approach to nonlinear differential equations”, Physica D, 69 (1993), 33–58 |
| 11. |
R. Conte, M. Musette, “Linearity inside nonlinearity: exact solutions to the complex
Ginzburg–Landau equation”, Physica D, 69 (1993), 1–17 |
| 12. |
M. Florjańczyk, L. Gagnon, “Exact solutions for a higher-order nonlinear Schrödinger equation”, Phys. Rev. A, 41 (1990), 4478–4485 |
| 13. |
M. Florjańczyk, L. Gagnon, “Dispersive-type solutions for the Eckhaus equation”, Phys. Rev. A, 45 (1992), 6881–6883 |
| 14. |
G.-H. Halphen, “Sur la réduction d'equations différentielles linéaires aux formes
intégrables”, Ocuvres, tome 3, Gauthier-Villars, Paris, 1921, 1–260 |
| 15. |
A. Kundu, “Landau–Lifshitz and higher order nonlinear systems gauge generated from
nonlinear Schrödinger type equations”, J. Math. Phys., 25 (1984), 3433–3438 |
| 16. |
M. Musette, “Nonlinear partial differential equations”, An introduction to methods of complex analysis and geometry for
classical mechanics and nonlinear waves, eds. D. Benest, C. Froeschlé, Éditions Frontiéres, Gif-sur-Yvette, 1994, 145–195 |
| 17. |
P. Painlevé, “Sur les équations différentielles du second ordre et d'ordre
supérieur dont I'intégrale générale est uniforme”, Acta Math., 25 (1902), 1–85 |
| 18. |
A. Pickering, “A new truncation in Painlevé analysis”, J. Phys. A, 26 (1993), 4395–4405 |
| 19. |
J. Weiss, M. Tabor, G. Carnevale, “The Painlevé property for partial differential equations”, J. Math. Phys., 24 (1983), 522–526 |