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pro vyhledávání: '"Shimomura, Shun"'
Autor:
Shimomura, Shun
For the fourth Painlev\'e transcendents we derive elliptic asymptotic representations, which were announced by late Professor Kapaev without proofs. Then we newly obtain related results including the correction function.
Comment: 44 pages
Comment: 44 pages
Externí odkaz:
http://arxiv.org/abs/2410.20347
Autor:
Shimomura, Shun
For the first Painlev\'e transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We present an explicit error bound of this asymptotic expression, which l
Externí odkaz:
http://arxiv.org/abs/2307.14639
Autor:
Shimomura, Shun
For the fifth Painlev\'e 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 present an explicit asymptotic formula for the error term of this express
Externí odkaz:
http://arxiv.org/abs/2307.01424
Autor:
Shimomura, Shun
For a general solution of the third Painlev\'e equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions.
Externí odkaz:
http://arxiv.org/abs/2211.00886
Autor:
Shimomura, Shun
For a general solution of the degenerate third Painlev\'e equation we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips along generic directions.
Externí odkaz:
http://arxiv.org/abs/2207.11495
Autor:
Shimomura, Shun
For the fifth Painlev\'e transcendents an asymptotic representation by the Jacobi $\mathrm{sn}$-function is presented in cheese-like strips along generic directions near the point at infinity. Its elliptic main part depends on a single integration co
Externí odkaz:
http://arxiv.org/abs/2012.07321
Akademický článek
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Autor:
Shimomura, Shun
Publikováno v:
SIGMA 14 (2018), 113, 50 pages
For the Schlesinger-type equation related to the fifth Painlev\'e equation (V) via isomonodromy deformation, we present a three-parameter family of matrix solutions along the imaginary axis near the point at infinity, and also the corresponding monod
Externí odkaz:
http://arxiv.org/abs/1804.10369
Autor:
Shimomura, Shun
For the fifth Painlev\'e equation, we present families of convergent series solutions near the origin and the corresponding monodromy data for the associated isomonodromy linear system. These solutions are of complex power type, of inverse logarithmi
Externí odkaz:
http://arxiv.org/abs/1602.08808
Akademický článek
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