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A01=Alexander R. Its
A01=Andrei A. Kapaev
A01=Athanassios S. Fokas
A01=Victor Yu. Novokshenov
Age Group_Uncategorized
Age Group_Uncategorized
Author_Alexander R. Its
Author_Andrei A. Kapaev
Author_Athanassios S. Fokas
Author_Victor Yu. Novokshenov
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Category1=Non-Fiction
Category=PBKJ
COP=United States
Delivery_Pre-order
Language_English
PA=Not yet available
Price_€100 and above
PS=Forthcoming
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Painleve Transcendents: The Riemann-Hilbert Approach

At the turn of the twentieth century, the French mathematician Paul Painleve and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painleve I-VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painleve transcendents (i.e., the solutions of the Painleve equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painleve equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painleve transcendents. This striking fact, apparently unknown to Painleve and his contemporaries, is the key ingredient for the remarkable applicability of these ``nonlinear special functions''. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painleve functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painleve equations and related areas. See more
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A01=Alexander R. ItsA01=Andrei A. KapaevA01=Athanassios S. FokasA01=Victor Yu. NovokshenovAge Group_UncategorizedAuthor_Alexander R. ItsAuthor_Andrei A. KapaevAuthor_Athanassios S. FokasAuthor_Victor Yu. Novokshenovautomatic-updateCategory1=Non-FictionCategory=PBKJCOP=United StatesDelivery_Pre-orderLanguage_EnglishPA=Not yet availablePrice_€100 and abovePS=Forthcomingsoftlaunch

Will deliver when available. Publication date 31 Mar 2024

Product Details
  • Publication Date: 31 Mar 2024
  • Publisher: American Mathematical Society
  • Publication City/Country: United States
  • Language: English
  • ISBN13: 9781470475567

About Alexander R. ItsAndrei A. KapaevAthanassios S. FokasVictor Yu. Novokshenov

Athanassios S. Fokas Cambridge University United Kingdom.Alexander R. Its Indiana University-Purdue University Indianapolis IN.Andrei A. Kapaev and Victor Yu. Novokshenov Russian Academy of Sciences Ufa Russia.

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