ELLIPTIC ASYMPTOTIC REPRESENTATION OF THE FIFTH PAINLEVÉ TRANSCENDENTS

For the fifth Painlevé transcendents, an asymptotic representation by Jacobi sn-function is presented in cheese-like strips along generic directions near point at infinity. Its elliptic main part depends on a single integration constant, which phase shift and parametrized monodromy data for associated isomonodromy deformation. In addition, under certain supposition, error term also expressed explicit formula, whose leading written terms of integrals ?-function, contains other constant. Instead justification scheme solutions Riemann-Hilbert problems Brouwer fixed theorem, we begin with boundedness property Lagrangian function, enables us to determine modulus satisfying Boutroux equations construct deductively representation.