A Riemann-Hilbert problem for an energy dependent Schrödinger operator

Inverse Problems

Volumn 12, Issue 6, 1996, Pages 1003-1025

  Sattinger, David H ^a   Szmigielski, Jacek ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001444209     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/12/6/014     Document Type: Article

References (17)

1. Beals R and Coifman R 1984 Scattering and inverse scattering for first order systems Commun. Pure Appl. Math. 37 39-90
2. Beals R and Coifman R 1985 Inverse scattering and evolution equations Commun. Pure Appl. Math. 38 29-42
3. Beals R, Deift P and Tomei C 1988 Direct and Inverse Scattering on the Line (Mathematical Surveys and Monographs 28) (Providence, RI: American Mathematical Society)
4. Camassa R and Holm D D 1993 An integrable shallow water equation with peaked solitons Phys. Rev. Lett. 71 1661-4
5. Deift P. Venakides S and Zhou X 1994 The collisionless shock region for the long-time behaviour of solutions of the KdV equation Commun. Pure Appl. Math. 47 199-206
6. Drazin P G and Johnson R S 1989 Solitons: An Introduction (Cambridge: Cambridge University Press)
7. Fordy A P 1990 Isospectral flows: Their Hamiltonian structures, Miura maps, and master symmetries Solitans Physics, Mathematics, and Nonlinear Optics (IMA Volumes in Mathematics and its Applications 25) ed P J Olver and D H Sattinger (New York: Springer) pp 97-121
8. Jaulent M 1972 On an inverse scattering problem with an energy dependent potential Ann. Inst. H. Poincaré A 17 363-72; 1976 Inverse scattering problem in absorbing media J. Math. Phys. 17 1351-60.
9. Jaulent M 1972 On an inverse scattering problem with an energy dependent potential Ann. Inst. H. Poincaré A 17 363-72; 1976 Inverse scattering problem in absorbing media J. Math. Phys. 17 1351-60.
10. Jaulent M and Jean C 1976 The inverse problem for the one-dimensional Schrödinger operator with an energy dependent potential, I, II Ann. Inst. H. Poincaré A 25 105-18, 119-37
11. Kaup D 1975 A higher-order water wave equation and the method of solving it Prog. Theor. Phys. 54 396-402
12. Matveev V B and Yavor M I 1979 Solutions presque périodiques et N-solitons de l'equation hydrodynamique non linéaire de Kaup Ann. Inst. H. Poincaré A 31 25-41
13. Novikov S P, Manakov S V, Pitatevksi L P and Zakharov V E 1985 Theory of Solitions (New York: Consultants Bureau)
14. Sachs R 1988 On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy Physica 30D 1-27; 1989 Polynomial τ-function for the AKNS hierarchy Proc. Symp. in Pure Mathematics vol 49, part 1 (Providence, RI: American Mathematical Society) pp 133-41
15. Sachs R 1988 On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy Physica 30D 1-27; 1989 Polynomial τ-function for the AKNS hierarchy Proc. Symp. in Pure Mathematics vol 49, part 1 (Providence, RI: American Mathematical Society) pp 133-41
16. Sattinger D H and Szmigielski J 1995 Energy dependent scattering theory Diff. Int. Eq. 8 945-59
17. Zakharov V E and Shabat A B 1972 Exact theory of two-diemensional self-focusing and one-diemensional self-modulation of waves in nonlinear media Sov. Phys.-JETP 34 62-9