New integrable equations of fourth order and higher degree related to Cosgrove's equation

Journal of Mathematical Physics

Volumn 42, Issue 4, 2001, Pages 1697-1707

  Gordoa, Pilar R ^a   Pickering, Andrew ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035531349     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1351886     Document Type: Article

References (11)

1. A. S. Fokas and M. J. Ablowitz, "On a unified approach to transformations and elementary solutions of Painlevé equations," J. Math. Phys. 23, 2033-2042 (1982).
2. A. Sakka and U. Muǧan, "Second-order second degree Painlevé equations related with Painlevé I, II, III equations," J. Phys. A 30, 5159-5177 (1997).
3. A. Sakka and U. Muǧan, "Second-order second-degree Painlevé equations related to Painlevé IV, V, VI equations," J. Phys. A 31, 2471-2490 (1998).
4. C. M. Cosgrove, "Higher order Painlevé equations in the polynomial class I. Bureau symbol P2," Stud. Appl. Math. 104, 1-65 (2000).
5. This ODE was first presented by Cosgrove at the Conference on Soliton Theory, PDEs, and Nonlinear Analysis, held at the University of New South Wales, Australia, 6-9 January 1997. An underlying linear problem was first presented by the current authors at the meeting Integrable Systems: Solutions and Transformations, held at Guardamar, Spain, 15-20 June 1998.
6. P. R. Gordoa and A. Pickering, "Bäcklund transformations for two new integrable partial differential equations," Europhys. Lett. 47, 21-24 (1999).
7. P. R. Gordoa and A. Pickering, "Non-isospectral scattering problems: a key to integrable hierarchies," J. Math. Phys. 40, 5749-5786 (1999).
8. P. R. Gordoa and A. Pickering, "On a new non-isospectral variant of the Boussinesq hierarchy," J. Phys. A 33, 557-567 (2000).
9. J. Chazy, "Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes," Acta Math. 34, 317-385 (1911).
10. R. Conte, A. P. Fordy, and A. Pickering, "A perturbative Painlevé approach to nonlinear differential equations," Physica D 69, 33-58 (1993).
11. U. Muǧan and A. Sakka, "Second-order second-degree Painlevé equations related with Painlevé I-VI equations and Fuchsian-type transformations," J. Math. Phys. 40, 3569-3587 (1999).