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|Title: ||On the connection formulas of Painlevé transcendents|
|Other Titles: ||Lun Panlewei fang cheng de lian jie gong shi|
|Authors: ||Zhang, Haiyu (張海愉)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Painlevé equations.|
|Notes: ||CityU Call Number: QA372 .Z44 2009|
ii, 100 leaves 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves -100)
|Abstract: ||The six Painleve equations were first discovered around the beginning of the
twentieth century by Painleve, Gambier and their colleagues in an investigation of nonlinear second-order ordinary differential equations. They are solutions
to certain nonlinear second-order ordinary differential equations in the complex
plane with the Painleve property (the only movable singularities are poles). They
are not generally solvable in terms of elementary functions.
Although first discovered from strictly mathematical considerations, the six
Painleve equations have arisen in a variety of important physical applications
including statistical mechanics, plasma physics, nonlinear waves, quantum gravity, quantum field theory, general relativity, nonlinear optics and fibre optics.
It is now becoming clear that the Painleve transcendents play the same role in
nonlinear mathematical physics that the clsssical special functions, such as Airy
functions, Bessel functions, etc., play in linear physics.
In this thesis, we use the method of "uniform asymptotics" proposed by
Bassom, Clarkson, Law and McLeod (Arch. Rat. Mech. Anal., 1998) to consider
the connection problem for the sine-Gordon PIII equation
which is the most commonly studied case among all general third Painleve transcendents.
Using the same method, we also provide a simpler and more rigorous proof of
the connection formulas of the Clarkson-McLeod solution for the fourth Painleve
which was established by Its and Kapaev (J. Phys. A: Math. Gen., 1998) via the
isomonodromy and Riemann Hilbert methods.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2374944|
|Appears in Collections:||MA - Doctor of Philosophy |
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