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Full characterisation of Painlevé V asymptotics and nonlinear monodromy-Stokes structure
Shun Shimomura
For a generic Painlevé V equation we characterise all the asymptotics in a right half plane near the point at infinity, that is, we find classified explicit solutions that are, by…
Kapaev's global asymptotics of the fourth Painlevé transcendents. Elliptic asymptotics
Shun Shimomura
For the fourth Painlevé transcendents we derive elliptic asymptotic representations, which were announced by late Professor Kapaev without proofs. Then we newly obtain related resu…
Explicit error term of the elliptic asymptotics for the first Painlevé transcendents
Shun Shimomura
For the first Painlevé transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We pr…
Two error bounds of the elliptic asymptotics for the fifth Painlevé transcendents
Shun Shimomura
For the fifth Painlevé equation it is known that a general solution is represented asymptotically by an elliptic function in cheese-like strips near the point at infinity. We prese…
Elliptic asymptotics for the complete third Painlevé transcendents
Shun Shimomura
For a general solution of the third Painlevé equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of th…
Boutroux ansatz for the degenerate third Painlevé transcendents
Shun Shimomura
For a general solution of the degenerate third Painlevé equation we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Weie…
Elliptic asymptotic representation of the fifth Painlevé transcendents
Shun Shimomura
For the fifth Painlevé transcendents an asymptotic representation by the Jacobi -function is presented in cheese-like strips along generic directions near the point at…
Three-Parameter Solutions of the PV Schlesinger-Type Equation near the Point at Infinity and the Monodromy Data
Shun Shimomura
For the Schlesinger-type equation related to the fifth Painlevé equation (V) via isomonodromy deformation, we present a three-parameter family of matrix solutions along the imagina…
Critical behaviours of the fifth Painlevé transcendents and the monodromy data
Shun Shimomura
For the fifth Painlevé equation, we present families of convergent series solutions near the origin and the corresponding monodromy data for the associated isomonodromy linear syst…