soliton theory

SearchAdvancedHelp

(0.001 seconds)

8 matching pages

1: 18.38 Mathematical Applications

… ►

Integrable Systems

… ►However, by using Hirota’s technique of bilinear formalism of soliton theory, Nakamura (1996) shows that a wide class of exact solutions of the Toda equation can be expressed in terms of various special functions, and in particular classical OP’s. …

2: 9.16 Physical Applications

… ►Details of the Airy theory are given in van de Hulst (1957) in the chapter on the optics of a raindrop. … ►Extensive use is made of Airy functions in investigations in the theory of electromagnetic diffraction and radiowave propagation (Fock (1965)). … ►These first appeared in connection with the equation governing the evolution of long shallow water waves of permanent form, generally called solitons, and are predicted by the Korteweg–de Vries (KdV) equation (a third-order nonlinear partial differential equation). The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics. … ►Reference to many of these applications as well as to the theory of elasticity and to the heat equation are given in Vallée and Soares (2010): a book devoted specifically to the Airy and Scorer functions and their applications in physics. …

3: Bibliography K

… ►

Replica field theories, Painlevé transcendents, and exact correlation functions. Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).

ⓘ

External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

Encodings:

BibTeX

… ►

Dark optical solitons: Physics and applications. Physics Reports 298 (2-3), pp. 81–197.

ⓘ

External Links:

Document

Referenced by:

§22.19(iii).

Encodings:

BibTeX

… ►

Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen. Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).

ⓘ

External Links:

ZentralBlatt

Referenced by:

§19.5.

Encodings:

BibTeX

… ►

Theorie und Anwendung der unendlichen Reihen. 4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).

ⓘ

Notes:

A translation by R. C. Young appeared in 1928, Theory and Application of Infinite Series, Blackie, 571pp.

External Links:

MathReview, ZentralBlatt

Referenced by:

§3.9(ii).

Encodings:

BibTeX

… ►

Zur Theorie der Modulformen $n$-ten Grades. I. Math. Z. 59, pp. 399–416 (German).

ⓘ

External Links:

ISSN 0025-5874, Document, MathReview (H. S. Zuckerman), ZentralBlatt

Referenced by:

§35.6(i).

Encodings:

BibTeX

…

4: Bibliography S

… ►

The Laplace Transform: Theory and Applications. Undergraduate Texts in Mathematics, Springer-Verlag, New York.

ⓘ

External Links:

ISBN 0-387-98698-7, MathReview (Philip Heywood), ZentralBlatt

Referenced by:

§1.14(iii), §1.14(vii).

Encodings:

BibTeX

… ►

Quantum defect theory. Rep. Prog. Phys. 46 (2), pp. 167–257.

ⓘ

External Links:

Document

Referenced by:

§33.14(i), §33.22(ii).

Encodings:

BibTeX

… ►

Characterization of Jacobian varieties in terms of soliton equations. Invent. Math. 83 (2), pp. 333–382.

ⓘ

External Links:

ISSN 0020-9910, Document, MathReview (Bert van Geemen), ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX

… ►

Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

Referenced by:

§3.9(vi).

Encodings:

BibTeX

… ►

Elliptic Solitons and Heun’s Equation. In The Kowalevski Property (Leeds, UK, 2000), V. B. Kuznetsov (Ed.), CRM Proc. Lecture Notes, Vol. 32, pp. 287–306.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§31.8.

Encodings:

BibTeX

…

5: 23.21 Physical Applications

§23.21 Physical Applications

… ►

§23.21(ii) Nonlinear Evolution Equations

… ►For applications to soliton solutions of the Korteweg–de Vries (KdV) equation see McKean and Moll (1999, p. 91), Deconinck and Segur (2000), and Walker (1996, §8.1). … ►

Quantum field theory. See Witten (1987).

… ►

String theory. See Green et al. (1988a, §8.2) and Polchinski (1998, §7.2).

6: Bibliography D

… ►

Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.

ⓘ

Notes:

Revised and with a preface by Hugh L. Montgomery

External Links:

ISBN 0-387-95097-4, MathReview, ZentralBlatt

Referenced by:

§27.12.

Encodings:

BibTeX

… ►

Pólya’s Theory of Counting. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), pp. 144–184.

ⓘ

External Links:

ISBN 0898741726

Referenced by:

§26.20.

Encodings:

BibTeX

… ►

The KP equation with quasiperiodic initial data. Phys. D 123 (1-4), pp. 123–152.

ⓘ

Notes:

Nonlinear waves and solitons in physical systems (Los Alamos, NM, 1997)

External Links:

ISSN 0167-2789, Document, MathReview (Pavel Krejčí), ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX

… ►

Elements of the Theory of Numbers. Harcourt/Academic Press, San Diego, CA.

ⓘ

External Links:

ISBN 0-12-209130-2, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.24.

Encodings:

BibTeX

… ►

Solitons: An Introduction. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 0-521-33389-X; 0-521-33655-4, MathReview (Peter A. Clarkson), ZentralBlatt

Referenced by:

§22.19(iii), Ch.22.

Encodings:

BibTeX

…

7: Bibliography H

… ►

Quantum theory for mathematicians. Graduate Texts in Mathematics, Vol. 267, Springer, New York.

ⓘ

External Links:

ISBN 978-1-4614-7115-8; 978-1-4614-7116-5, Document, Link, MathReview Entry

Referenced by:

§1.18(x).

Encodings:

BibTeX

… ►

An Introduction to the Theory of Numbers. 5th edition, The Clarendon Press Oxford University Press, New York-Oxford.

ⓘ

External Links:

ISBN 0-19-853170-2; 0-19-853171-0, MathReview (T. M. Apostol), ZentralBlatt

Referenced by:

§20.12(i), Ch.27.

Encodings:

BibTeX

… ►

Optical Solitons in Fibers. Springer-Verlag, Berlin, Germany.

ⓘ

External Links:

ISBN 0387506683

Referenced by:

§22.19(iii).

Encodings:

BibTeX

… ►

Molecular Electronic-Structure Theory. John Wiley & Sons, New York.

ⓘ

Notes:

Paperback Reprint of 2004 Edition

External Links:

ISBN 9871118531471

Referenced by:

§18.39(iii).

Encodings:

BibTeX

… ►

The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.

ⓘ

Notes:

Reprinted by Chelsea Publishing Company, New York, 1955 and 1965.

External Links:

ISBN 0-8284-0104-7, MathReview, ZentralBlatt

Referenced by:

§14.1, §14.11, §14.16(ii), §14.16(iii), §14.20(x), §14.27, §14.27, §14.3(i), §14.3(i), Ch.14, §29.18(iii), Ch.29.

Encodings:

BibTeX

…

8: Bibliography

… ►

Solitons, Nonlinear Evolution Equations and Inverse Scattering. London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 0-521-38730-2, Document, Link, MathReview (Walter Oevel), ZentralBlatt

Referenced by:

§22.19(ii), §22.19(iii), §32.11(ii), §32.5, §9.16, Profile Mark J. Ablowitz, Profile Peter A. Clarkson.

Encodings:

BibTeX

… ►

Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

ⓘ

External Links:

ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

Referenced by:

§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

Encodings:

BibTeX

… ►

Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

ⓘ

Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

External Links:

MathReview, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

►

Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

ⓘ

Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

Encodings:

BibTeX

… ►

Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

ⓘ

Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

Encodings:

BibTeX

…