RUS  ENG
Полная версия
ЖУРНАЛЫ // Теоретическая и математическая физика

ТМФ, 1994, том 99, номер 2, страницы 226–233 (Mi tmf1581)

Exact solutions to the partially integrable Eckhaus equation
R. Conte, M. Musette

Список литературы

1. F. J. Bureau, “Integration of some nonlinear systems of ordinary differential equations”, Ann. Mat. Pura Appl. (4), 94 (1972), 345–359  crossref  mathscinet  zmath
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  mathscinet  zmath
3. F. Calogero, W. Eckhaus, “Nonlinear evolution equations, rescalings, model PDEs and their integrability. I”, Inverse problems, 3 (1987), 229–262  crossref  mathscinet  zmath  adsnasa
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  crossref  mathscinet  zmath  adsnasa
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  crossref  mathscinet  zmath
6. P. A. Clarkson, “Dimensional reductions and exact solutions of a generalized nonlinear Schrödinger equation”, Nonlinearity, 5 (1992), 453–472  crossref  mathscinet  zmath  adsnasa
7. P. A. Clarkson, C. M. Cosgrove, “The Painlevé property and a generalised derivative nonlinear Schrödinger equation”, J. Phys. A, 20 (1987), 2003–2024  crossref  mathscinet  zmath  adsnasa
8. R. Conte, “Invariant Painlevé analysis of partial differential equations”, Phys. Lett. A, 140 (1989), 383–390  crossref  mathscinet  adsnasa
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  crossref  mathscinet  zmath
10. R. Conte, A. P. Fordy, A. Pickering, “A perturbative Painleve approach to nonlinear differential equations”, Physica D, 69 (1993), 33–58  crossref  mathscinet  zmath  adsnasa
11. R. Conte, M. Musette, “Linearity inside nonlinearity: exact solutions to the complex Ginzburg–Landau equation”, Physica D, 69 (1993), 1–17  crossref  mathscinet  zmath  adsnasa
12. M. Florjańczyk, L. Gagnon, “Exact solutions for a higher-order nonlinear Schrödinger equation”, Phys. Rev. A, 41 (1990), 4478–4485  crossref  adsnasa
13. M. Florjańczyk, L. Gagnon, “Dispersive-type solutions for the Eckhaus equation”, Phys. Rev. A, 45 (1992), 6881–6883  crossref  adsnasa
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  crossref  mathscinet  adsnasa
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  mathscinet  zmath  adsnasa
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  crossref  mathscinet
18. A. Pickering, “A new truncation in Painlevé analysis”, J. Phys. A, 26 (1993), 4395–4405  crossref  mathscinet  zmath  adsnasa
19. J. Weiss, M. Tabor, G. Carnevale, “The Painlevé property for partial differential equations”, J. Math. Phys., 24 (1983), 522–526  crossref  mathscinet  zmath  adsnasa


© МИАН, 2026