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Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
Local Symplectic Filling Obstructions Contact 3-Manifolds
2010/12/6
We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose i...
Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
Non-Hamiltonian dispersionless 2DTL hierarchy
2010/4/2
We consider two-component integrable generalizations of the dispersionless 2DTL hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hi...