Claeys, Tom
[UCL]
Vanlessen, M
[]
We establish the existence of a real solution y( x, T) with no poles on the real line of the following fourth order analogue of the Painleve I equation: x = T y - (1/6y(3) + 1/24(y(x)(2) +2yy(xx)) + 1/240y(xxxx)). This proves the existence part of a conjecture posed by Dubrovin. We obtain our result by proving the solvability of an associated Riemann-Hilbert problem through the approach of a vanishing lemma. In addition, by applying the Deift/Zhou steepest-descent method to this Riemann-Hilbert problem, we obtain the asymptotics for y( x, T) as x -> +/-infinity.
Bibliographic reference |
Claeys, Tom ; Vanlessen, M. The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation . In: Nonlinearity, Vol. 20, no. 5, p. 1163-1184 (2007) |
Permanent URL |
http://hdl.handle.net/2078/73338 |