How Long to Read Painleve Transcendents

How Long Does it Take to Read Painleve Transcendents?

It takes the average reader to read Painleve Transcendents by ATHANASSIOS S. FOKAS

Assuming a reading speed of 250 words per minute. Learn more

Description

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.

How long is Painleve Transcendents?

Painleve Transcendents by ATHANASSIOS S. FOKAS is 0 pages long, and a total of 0 words.

This makes it 0% the length of the average book. It also has 0% more words than the average book.

How Long Does it Take to Read Painleve Transcendents Aloud?

The average oral reading speed is 183 words per minute. This means it takes to read Painleve Transcendents aloud.

What Reading Level is Painleve Transcendents?

Painleve Transcendents is suitable for students ages 2 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Painleve Transcendents?

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