Method With Nonzero Background Potential. Application to Inverse Scattering for the

References

• Ablowitz , M.J. , Bar Yaacov , D. and Fokas , A.S. 1983 . On the inverse scattering transform for the Kadomtsev—Petviashvili equation, . Stud. Appl. Math. , 69 : 135 – 143 .
   Web of Science ®Google Scholar
• Alessandrini , G. 1988 . Stable determination of conductivity by boundary measurements . Applic.Analysis , 27 : 153 – 172 .
   Google Scholar
• R. Beals and R. R. Coifman, Scattering, transformations spectrales et equations d'evolution non linéaires I,II,(Siminaire Goulaonic—Meyer—Schwartz 1980–1981, Exposé22, 1981–1982, Exposé21, EéxposeéPolytechnique,Palaiseau.
   Google Scholar
• Beals , R. and Coifman , R.R . 1985 . Multidimensional inverse scattering and nonlinear partial differential equations . Proc. Symp. Pure Math. , 43 : 45 – 70 .
   Google Scholar
• Boiti , M. , Leon , J. , Manna , M. and Pempinelli , F. 1987 . On a spectral transform of a KdV—like equation related to the Schrōdinger operato in the plane . Inverse Proglems , 3 : 25 – 36 .
   Web of Science ®Google Scholar
• Boiti , M. , Pempinelli , F. and Pogrebkov , A.K. 1994 . SOme new methods and results in the theory of (2+–dimensional integrable equations . Teroret. i Matemat. Fizika , 99 : 185 – 200 .
   Google Scholar
• Calogero , F. 1982 . “ Solutions oand the Spectral Transform ” . Edited by: DeGasperis , A. North—Holland , Amsterdam
   Google Scholar
• Daddeev , L.D. 1976 . Inverse proglem of quantum scattering theory II Sovremennye problemy mat. Viniti Mascow . Translation in J.Sov.Math. , 5 : 334 – 396 .
   Google Scholar
• Grinevich , R.G. and Novikov , P.G. 1995 . Transparent potentials at fized energy in dimension two. . Fized—energy dispersion relations for the fast decaying potentials, Commun. Math. Phys. , 174 : 409 – 446 .
   Web of Science ®Google Scholar
• P. G. Grinevich and S. P. Novikov, Two—dimensional “inverse scattering problem”for negative energies and generalized—analytic functions. I. Energies below the ground state, Funkts. Anal. i Pril. 22(1) (1988), 23–33,translation in Funct.Ana1. and Appl. 22 (1988), 19–27.
   Google Scholar
• Henkin , G.M. 1980 . The representation of the Yang—Mills equations in the form of the Cauchy—Riemann equations on the twister space . Dokl. Akad. Nauk SSSR , 255 : 844 – 847 .
   Google Scholar
• Henkin , G.M. and Novikov , R.G. 1988 . A Multidimensional inverse problem in quantum and acoustic scattering . Inverse Problems , 4 : 103 – 121 .
   Web of Science ®Google Scholar
• S. P. Merkuriev and L. D. Faddeev, Quantum Scattering Theory for Systems of Several Particles, Nauka,Moscow,l985 (in Russian)
   Google Scholar
• A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Preprint,l993.
   Google Scholar
• Nachman , A.I. and Ablowitz , M.J. 1984 . A multidimensional inverse scattering method . Stud.Appl. Math. , 71 : 243 – 250 .
   Web of Science ®Google Scholar
• R. G. Novikov, Miltidimensional inverse scattering problem for acoustic equation, Preprint 32M Institute of Physics, Krasnojarsk, 1986, (in Russian)
   Google Scholar
• Novikov , R.G. 1992 . The inverse scattering problem on a fized energy level for the two—dimensional Schrōdinger operator . J.Funct.Anal , 103 : 409 – 463 .
   Web of Science ®Google Scholar
• R. G. Novikov and G. M. Henkin, The –equation in the multidimensional inverse scattering problem, a)Preprint 27M Institute of Physics, Krasnojarsk, 1986 (in Russian b)Uspekhi Math.Nauk 42(3) (1987), 93–151, translation in Russ.Math.Surv. 42(4) (1987), 109–180.
   Google Scholar
• Stefanov , P, . 1990 . A uniqueness result for the inverse back—scattering proglem . Inverse Problem , 6 : 1055 – 1064 .
   Web of Science ®Google Scholar
• Sun , Z. and Uhlmann , G. 1993 . Recovery of singularities for formaly determined inverse problems . Commun.Math.Phys. , 153 : 431 – 445 .
   Web of Science ®Google Scholar
• T. Y. Tsai, The Schrōdinger operator in the plane , Dissertation, Yale University, 1989.
   Google Scholar
• I. N. Vekua, Generalized Analytic Functions, Perganlon Press, Oxford, 1962.
   Google Scholar
• Grinevich , P.G. 1989 . Fast decreasing potentials at the finite—gap background and the problem on Riemann surfaces, . Funkts. Anal. i Pril. , 23 ( 4 ) : 79 – 80 .
   Google Scholar
• R. G. Novikov, method with nonzero background potential. Application to inverse scattering for the two—dimensional acoustic equation, Preprint, Universiteéde Nantes, 1994.
   Google Scholar