nonlinear equations

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21: 3.3 Interpolation

… ►It can be used for solving a nonlinear scalar equation $f(z)=0$ approximately. …

22: Bibliography I

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On the asymptotic analysis of the Painlevé equations via the isomonodromy method. Nonlinearity 7 (5), pp. 1291–1325.

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External Links:

ISSN 0951-7715, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.11(iii).

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23: Alexander A. Its

… ►Books by Its are The Isomonodromic Deformation Method in the Theory of Painlevé Equations (with V. … Novokshënov), published by Springer in 1986, Algebro-geometric Approach to Nonlinear Integrable Problems (with E. …

24: 18.38 Mathematical Applications

… ►While the Toda equation is an important model of nonlinear systems, the special functions of mathematical physics are usually regarded as solutions to linear equations. …

25: Alexander I. Bobenko

… ►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E. … Matveev), published by Springer in 1994, Painlevé Equations in the Differential Geometry of Surfaces (with U. …

26: 15.8 Transformations of Variable

… ►A necessary and sufficient condition that there exists a quadratic transformation is that at least one of the equations shown in Table 15.8.1 is satisfied. … ►The hypergeometric functions that correspond to Groups 3 and 4 have a nonlinear function of $z$ as variable. … ►In the equations that follow in this subsection all functions take their principal values. …

27: Bibliography W

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Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

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ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

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Solutions of the fifth Painlevé equation. I. Hokkaido Math. J. 24 (2), pp. 231–267.

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ISSN 0385-4035, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.10(v).

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Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series. Computer Physics Reports 10 (5-6), pp. 189–371.

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Document

Referenced by:

§2.11(vi), §3.9(v), §3.9(vi).

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Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations. Computers in Physics 10 (5), pp. 496–503.

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Document

Referenced by:

§2.11(vi), §2.11(vi).

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Linear and Nonlinear Waves. John Wiley & Sons, New York.

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Notes:

Reprinted in 1999.

External Links:

ISBN 0471359424, MathReview, ZentralBlatt

Referenced by:

§9.16.

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28: 32.7 Bäcklund Transformations

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§32.7(ii) Second Painlevé Equation

… ►The solutions $w_{\alpha }=w(z;\alpha )$, $w_{\alpha \pm 1}=w(z;\alpha \pm 1)$, satisfy the nonlinear recurrence relation … ►

§32.7(iii) Third Painlevé Equation

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§32.7(iv) Fourth Painlevé Equation

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29: Bibliography M

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On reducing the Heun equation to the hypergeometric equation. J. Differential Equations 213 (1), pp. 171–203.

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ISSN 0022-0396, Document, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§31.7(i).

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The 192 solutions of the Heun equation. Math. Comp. 76 (258), pp. 811–843.

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ISSN 0025-5718, Document, MathReview (Wadim Zudilin), ZentralBlatt (Masaaki Yoshida)

Referenced by:

§31.3(iii).

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Rational solutions of the Painlevé VI equation. J. Phys. A 34 (11), pp. 2281–2294.

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ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.8(vi).

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Picard and Chazy solutions to the Painlevé VI equation. Math. Ann. 321 (1), pp. 157–195.

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ISSN 0025-5831, Document, MathReview, ZentralBlatt

Referenced by:

§32.9(iii).

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The Second Painlevé Transcendent: A Nonlinear Airy Function. In Mechanics Today, Vol. 5, pp. 297–313.

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External Links:

MathReview (H. E. Fettis), ZentralBlatt

Referenced by:

§32.11(ii), §32.17, §32.3(ii).

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30: Bibliography P

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Sur les équations différentielles du second ordre à points critiques fixès. C.R. Acad. Sc. Paris 143, pp. 1111–1117.

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External Links:

ZentralBlatt

Referenced by:

§32.2(iv).

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Smoothing of the Stokes phenomenon for high-order differential equations. Proc. Roy. Soc. London Ser. A 436, pp. 165–186.

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ISSN 0962-8444, FullText, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.11(v).

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A uniform asymptotic expansion for the incomplete gamma function. J. Comput. Appl. Math. 148 (2), pp. 323–339.

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ISSN 0377-0427, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

(8.11.6), §8.11(iii), (8.12.18), §8.12, §8.12, §8.12, Erratum (V1.0.16) for Equation (8.12.18).

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Evaluation of Fermi-Dirac Integral. In Nonlinear Numerical Methods and Rational Approximation (Wilrijk, 1987), A. Cuyt (Ed.), Mathematics and Its Applications, Vol. 43, pp. 435–444.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§25.18(i).

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Remarks on computing the probability integral in one and two dimensions. In Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, 1945, 1946, pp. 63–78.

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External Links:

MathReview (L. A. Aroian), ZentralBlatt

Referenced by:

(7.8.8), §7.8, Erratum (V1.0.17) for Equation (7.8.8).

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