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|Title:||Okamoto's space for the first Painlevé equation in Boutroux coordinates|
|Authors:||Duistermaat, Johannes (Hans) J.|
The first Painlevé equation
|Citation:||Duistermaat JJ and Joshi N (2011) Okamoto's Space for the First Painlevé Equation in Boutroux Coordinates. Archive for Rational Mechanics and Analysis, 202(3), 707–785.|
|Abstract:||We study the completeness and connectedness of asymptotic behaviours of solutions of the first Painlev ́e equation d^2 y/ dx^2 = 6 y^2 + x, in the limit x → ∞, x ∈ C. This problem arises in various physical contexts including the critical behaviour near gradient catastrophe for the focusing nonlinear Schrodinger equation. We prove that the complex limit set of solutions is non-empty, compact and invariant under the flow of the limiting autonomous Hamiltonian system, that the infinity set of the vector field is a repellor for the dynamics and obtain new proofs for solutions near the equilibrium points of the autonomous flow. The results rely on a realization of Okamoto’s space, i.e., the space of initial values compactified and regularized by embedding in CP2 through an explicit construction of nine blow-ups.|
|Rights and Permissions:||The original publication is available at www.springerlink.com.|
|Type of Work:||Article|
|Type of Publication:||Post-print|
|Appears in Collections:||Research Papers and Publications. Mathematics and Statistics|
Research Papers and Publications. Science
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