A hypergeometric function approach to the persistence problem of single sine-gordon breathers

Transactions of the American Mathematical Society

Volumn 349, Issue 10, 1997, Pages 4053-4083

  Denzler, Jochen ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Breather; Hypergeometric function; Laplace transform; Saddle point analysis; Sine gordon equation

Indexed keywords

EID: 21944443727     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01951-x     Document Type: Article

References (19)

1. M. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions, Dover Publ. 1966 MR 34:8606
2. B. Birnir, H. McKean, A. Weinstein: The Rigidity of Sine-Gordon Breathers, Comm. Pure Appl. Math., 47 (1994), 1043-1051 MR 95h:35195
3. N. Bleistein: Uniform Asymptotic Expansions of Integrals with Stationary Point Near Algebraic Singularity, Comm. Pure Appl. Math., 19 (1966), 353-370 MR 34:4778
4. T.M. Cherry: Uniform asymptotic formulae for functions with transition points, Trans. AMS 68 (1950),224-257 MR ll:596b
5. C. Chester, B. Friedman, F. Ursell: An extension of the method of steepest descents, Proc. of the Cambridge Philosophical Society 53 (1957), 599-611 MR 19:853a
6. J. Denzler: Nonpersistence of Breathers for the Perturbed Sine Gordon Equation, PhD thesis number 9954, ETH Zürich, Switzerland, 1992. Copy available from the author
7. J. Denzler: Nonpersistence of Breather Families for the Perturbed Sine Gordon Equation, Comm. Math. Phys 158 (1993), 397-430 MR 95c:35210
8. J. Denzler: Second Order Nonpersistence of the Sine Gordon Breather Under an Exceptional Perturbation, Annales de l'Institut Henri Poincaré, Analyse Non Linéaire 12 (1995), 201-239 MR 96b:35188
9. G. Doetsch: Handbuch der Laplace-Transformationen, Birkhäuser 1950 MR 13:230f
10. B. Friedman: Stationary phase with neighboring critical points, SIAM Journal (later SIAM J. on Appl. Math.) 7 (1959), 280-289 MR 22:159
11. Gradshteyn, Ryzhik: Table of Integrals, Series, and Products, Academic Press, 1965/1980 MR 33:5952; MR 81g:33001
12. N. Hayek, B.J. Gonzalez, E.R. Negrin: Abelian Theorems for the Index afi-transform, Revista Técnica de la Facultad Ingenieria, Universidad del Zulia, Maracaibo, Venezuela; 15 (1992), 167-171 MR 93m:44003
13. Ch. Müntz: Über den Approximationssatz von Weierstraß; in: Mathematische Abhandlungen, Hermann Amandus Schwarz zu seinem fünzigjährigen Doktorjubiläum, Springer 1914
14. O. Perron: Über die näherungsweise Berechnung von Funktionen großer Zahlen, Sitzungsberichte der Königlich Bayerischen Akademie der Wissenschaften, MathematischNaturwissenschaftliche Klasse (1917), 191-219
15. H. Seifert: Die hypergeometrischen Differentialgleichungen der Gasdynamik, Mathematische Annalen 120 (1947),75-126 MR 9:350c
16. H.M. Srivastava, R.G. Buschman: Convolution Integral Equations with Special Function Equations, Wiley Eastern Limited, New Delhi, 1977 MR 58:29888
17. D.V. Widder: The Laplace Transform, Princeton University Press, 1941 MR 3:232d
18. J. Wimp: A Class of Integral Transforms, Proc. Edinburgh Math. Soc. 14 (1964), 33-40 MR 29:1503
19. S.B. Yakubovich, Vu Kim Tuan, O.I. Marichev, S.L. Kalla: A Class of Index Integral Transforms, Rev. Tec. Ing ... (see [12]), 10 (1987), 105-118. MR 89a:44012