Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 36 (1982) no. 1, pp. 41-58.
@article{AIHPA_1982__36_1_41_0,
author = {Graffi, S. and Harrell, E.},
title = {Inverse scattering for the one-dimensional {Stark} effect and application to the cylindrical {KdV} equation},
journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
pages = {41--58},
publisher = {Gauthier-Villars},
volume = {36},
number = {1},
year = {1982},
zbl = {0506.35079},
mrnumber = {653017},
language = {en},
url = {http://archive.numdam.org/item/AIHPA_1982__36_1_41_0/}
}
TY  - JOUR
AU  - Graffi, S.
AU  - Harrell, E.
TI  - Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
JO  - Annales de l'institut Henri Poincaré. Section A, Physique Théorique
PY  - 1982
DA  - 1982///
SP  - 41
EP  - 58
VL  - 36
IS  - 1
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1982__36_1_41_0/
UR  - https://zbmath.org/?q=an%3A0506.35079
UR  - https://www.ams.org/mathscinet-getitem?mr=653017
LA  - en
ID  - AIHPA_1982__36_1_41_0
ER  - 
%0 Journal Article
%A Graffi, S.
%A Harrell, E.
%T Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
%J Annales de l'institut Henri Poincaré. Section A, Physique Théorique
%D 1982
%P 41-58
%V 36
%N 1
%I Gauthier-Villars
%G en
%F AIHPA_1982__36_1_41_0
Graffi, S.; Harrell, E. Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 36 (1982) no. 1, pp. 41-58. http://archive.numdam.org/item/AIHPA_1982__36_1_41_0/

[1] W. Hunziker, Schrödinger Operators with Electric or Magnetic Fields, in Mathematical Problems in theoretical Physics, K. Osterwalder, ed. Lecture Notes in Physics, t. 116, Berlin, Heidelberg, and New York, Springer, 1980. | MR | Zbl

[2] I. Herbst, Schrödinger Operators with External Homogeneous Electric and Magnetic Fields, Lecture at the 1980 Erice Summer School in Mathematical Physics, to be published.

[3] E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, t. I, Oxtord, at the Clarendon Press, 1946. | Zbl

[4] J.E. Avron and I. Herbst, Spectral and Scattering Theory of Schrödinger Operators Related to the Stark Effect, Comm. Math. Physics, t. 52, 1977, p. 239-254. | MR | Zbl

[5] I. Herbst, Unitary Equivalence of Stark Hamiltonians, Math. Z., t. 155, 1977, p. 55-70. | MR | Zbl

[6] F. Calogero and A. Degasperis, Inverse Spectral Problem for the One-Dimensional Schrödinger Equation with an Additional Linear Potential, Lett. al Nuovo Cim., t. 23, 1978, p. 143-149.Solution by the Spectral-Transform Method of a Nonlinear Evolution Equation Including as a Special Case the Cylindrical KdV, ibid., p. 150-154.Conservation Laws for a Nonlinear Evolution Equation that Includes as a Special Case the Cylindrical KdV Equation, ibid., p. 155-160. | MR

[7] E. Hille, Ordinary Differential Equations in the Complex Domain, New York, Wiley, 1976. | MR | Zbl

[8] F.W.J. Olver, Asymptotics and Special Functions, New York, Academic Press, 1974. | MR | Zbl

[9] P.P. Kulish, Obratnaya Zadacha Rasseyaniya dlya Uravneniya Shredingera na Osi, Mat. Zametki, t. 4, 1968, p. 677-684.

[10] L.D. Faddeyev, The Inverse Problem in the Quantum Theory of Scattering, J. Math. Physics, t. 4, 1963, p. 72-104. | MR | Zbl

[11] M. Abramowitz and I.A. Stegun, eds. Handbook of Mathematical Functions, Applied Mathematics Series, t. 55, Washington, National Bureau of Standards, 1964.

[12] M. Reed and B. Simon, Methods of Modern Mathematical Physics, t. 2, Fourier Analysis, Self-Adjointness, New York, Academic Press, 1975. | Zbl

[13] D.V. Widder, The Airy Transform, Amer. Math. Monthly, t. 86, 1979, p. 271-277. | MR | Zbl

[14] R.K. Bullough and P.J. Caudrey, eds. Solitons, Topics in Current Physics, t. 17, Berlin, Heidelberg and New York, Springer, 1980. | MR | Zbl