Painleve Transcendents: The Riemann-hilbert Approach (Mathematical Surveys and Monographs)

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9780821836514: Painleve Transcendents: The Riemann-hilbert Approach (Mathematical Surveys and Monographs)

At the turn of the twentieth century, the French mathematician Paul Painlevé 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 Painlevé 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 Painlevé transcendents (i.e., the solutions of the Painlevé 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 Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé 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 Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Pa

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The book is indispensable for both students and researchers working in the field. The authors include all necessary proofs of the results and the background material and, thus, the book is easy to read. --Mathematical Reviews

The book by Fokas et al. is a comprehensive, substantial, and impressive piece of work. Although much of the book is highly technical, the authors try to explain to the reader what they are trying to do. ... This book complements other monographs on the Painlevi equations. --Journal of Approximation Theory

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Athanassios S. Fokas; Alexander R. Its; Andrei A. Kapaev; and Victor Yu. Novokshenov
Editore: American Mathematical Society (2006)
ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society, 2006. Hardcover. Condizione libro: New. Brand new. We distribute directly for the publisher. At the turn of the twentieth century, the French mathematician Paul Painlevé 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 Painlevé 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 Painlevé transcendents (i.e., the solutions of the Painlevé 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 Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé 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 Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas. Codice libro della libreria 1006230037

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Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev
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ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society, United States, 2006. Hardback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821836514

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Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev
Editore: American Mathematical Society, United States (2006)
ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society, United States, 2006. Hardback. Condizione libro: New. Language: English . Brand New Book. 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. Codice libro della libreria AAN9780821836514

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Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev, Victor Yu Novokshenov
Editore: American Mathematical Society
ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society. Hardback. Condizione libro: new. BRAND NEW, Painleve Transcendents: The Riemann-Hilbert Approach, Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev, Victor Yu Novokshenov, 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. Codice libro della libreria B9780821836514

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Athanassios S. Fokas, Alexander R. Its, Andrei A. Kapaev, and Victor Yu. Novokshenov
Editore: American Mathematical Society (2006)
ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society, 2006. Hardcover. Condizione libro: New. Codice libro della libreria DADAX082183651X

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Athanassios S. Fokas; Alexander R. Its; Andrei A. Kapaev; Victor Yu. Novokshenov
Editore: American Mathematical Society (2006)
ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro American Mathematical Society, 2006. Hardcover. Condizione libro: New. book. Codice libro della libreria 082183651X

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Athanassios S. Fokas; Alexander R. Its; Andrei A. Kapaev; Victor Yu. Novokshenov
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218365140000000

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Fokas, A. S. (Editor)/ Its, Alexander R./ Kapaev, Andrei A./ Novokshenov, Victor Yu
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ISBN 10: 082183651X ISBN 13: 9780821836514
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Descrizione libro Amer Mathematical Society, 2006. Hardcover. Condizione libro: Brand New. illustrated edition. 560 pages. 10.25x7.25x1.25 inches. In Stock. Codice libro della libreria __082183651X

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