M. J. Ablowitz and P. A. Clarkson, Solitons, evolution equations and inverse scattering, 1991.
DOI : 10.1017/CBO9780511623998

L. V. Bogdanov, The Veselov-Novikov equation as a natural generalization of the Korteweg-de Vries equation, Teoret. Mat. Fiz. Translation in Theoret. and Math. Phys, vol.70, issue.702, pp.309-314, 1987.

M. Boiti, J. J. Leon, M. Manna, and F. Pempinelli, On a spectral transform of a KDV-like equation related to the Schrodinger operator in the plane, Inverse Problems, vol.3, issue.1, pp.25-36, 1987.
DOI : 10.1088/0266-5611/3/1/008

M. Boiti, J. J. Leon, L. Martina, and F. Pempinelli, Scattering of localized solitons in the plane, Physics Letters A, vol.132, issue.8-9, pp.432-439, 1988.
DOI : 10.1016/0375-9601(88)90508-7

A. P. Calderón, On an inverse boundary problem. Seminar on Numerical Analysis and its Applications to Continuum Physics, pp.61-73, 1980.

J. Chang, The Gould-Hopper polynomials in the Novikov-Veselov equation, Journal of Mathematical Physics, vol.52, issue.9, p.92703, 2011.
DOI : 10.1063/1.3638043

A. De-bouard and J. C. Saut, Solitary waves of generalized Kadomtsev-Petviashvili equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.14, issue.2, pp.211-236, 1997.
DOI : 10.1016/S0294-1449(97)80145-X

A. De-bouard and J. Saut, Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves, SIAM Journal on Mathematical Analysis, vol.28, issue.5, pp.1064-1085, 1997.
DOI : 10.1137/S0036141096297662

V. G. Dubrovsky and I. Formusatik, New lumps of Veselov???Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schr??dinger equation via -dressing method, Physics Letters A, vol.313, issue.1-2, pp.68-76, 2003.
DOI : 10.1016/S0375-9601(03)00715-1

L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR Translation in Sov. Phys. Dokl, vol.165, issue.10, pp.514-517, 1965.

L. D. Faddeev, The inverse problem in the quantum theory of scattering. II. Itogi Nauki i Tekhniki, Ser. Sovrem. Probl. Mat. Dokl. Akad. Nauk SSSR Translation in J. Math. Sciences, vol.3, issue.53, pp.93-180, 1966.

M. V. Fedoryuk, Asymptotics : integrals and series, Moscow : Nauka, Mathematical Reference Library, 1987.

A. S. Fokas and M. J. Ablowitz, On the inverse scattering of the time?dependent Schrödinger equation and the associated Kadomtsev?Petviashvili (I) equation, Studies in Appl. Math, pp.69-211, 1983.

A. S. Fokas and P. M. Santini, Coherent structures in multidimensions, Physical Review Letters, vol.63, issue.13, pp.1329-1333, 1983.
DOI : 10.1103/PhysRevLett.63.1329

J. Françoise and R. G. Novikov, Rational solutions of KdV?type equations in dimension 2 + 1 and m?body problems on the line, C.R. Acad. Sci. Paris Sér. I Math, vol.314, issue.2, pp.109-113, 1992.

S. A. Gabov, Introduction to the theory of non?linear waves, 1988.

C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for Solving the Korteweg-deVries Equation, Physical Review Letters, vol.19, issue.19, pp.1095-1097, 1967.
DOI : 10.1103/PhysRevLett.19.1095

C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Korteweg-de Vries equation and generalizations. VI. Methods for exact solution, Comm. Pure Appl. Math, pp.27-97, 1974.

I. M. Gelfand, Some aspects of functional analysis and algebra, Proceedings of the International Congress of Mathematicians, pp.253-276, 1954.
DOI : 10.1007/978-3-642-61705-8_1

I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Moscow : Nauka, 1965.

P. G. Grinevich, Rational solitons of the Veselov?Novikov equation are reflectionless potentials at fixed energy, Teoret. Mat. Fiz. Translation in Theor. Math. Phys, vol.69, issue.2, pp.307-310, 1986.

P. G. Grinevich, Scattering transformation at fixed non-zero energy for the two-dimensional Schr??dinger operator with potential decaying at infinity, Russian Mathematical Surveys, vol.55, issue.6, pp.1015-1083, 2000.
DOI : 10.1070/RM2000v055n06ABEH000333

P. G. Grinevich and S. V. Manakov, Inverse problem of scattering theory for the two-dimensional Schrödinger operator, the ¯ ?-method and nonlinear equations

. Anal and . Prilozh, Translation in Funct, Anal. Appl, vol.20, issue.202, pp.14-24, 1986.

P. G. Grinevich and R. G. Novikov, Analogues of multisoliton potentials for the two-dimensional Schrödinger operator, and a nonlocal Riemann problem, Dokl. Akad. Nauk SSSR Translation in Sov. Math. Dokl, vol.286, issue.331, pp.19-22, 1986.

P. G. Grinevich and R. G. Novikov, Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials, Communications in Mathematical Physics, vol.7, issue.1,2, pp.409-446, 1995.
DOI : 10.1007/BF02099609

P. G. Grinevich and R. G. Novikov, Faddeev eigenfunctions for point potentials in two dimensions, Physics Letters A, vol.376, issue.12-13, pp.12-13, 2012.
DOI : 10.1016/j.physleta.2012.02.025

URL : https://hal.archives-ouvertes.fr/hal-00632264

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, Functional Analysis and Its Applications, vol.42, issue.3, pp.23-33, 1988.
DOI : 10.1007/BF01077719

N. Hayashi, P. I. Naumkin, and J. Saut, Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev-Petviashvili Equation, Communications in Mathematical Physics, vol.201, issue.3, pp.577-590, 1999.
DOI : 10.1007/s002200050569

G. M. Henkin and R. G. Novikov, The ¯ ?-equation in the multidimensional inverse scattering problem, Uspekhi Mat. Nauk Translation in Russ. Math. Surv, vol.42, issue.423, pp.93-152, 1987.

M. S. Joshi, S. Barreto, and A. , Recovering Asymptotics of Short Range Potentials, Communications in Mathematical Physics, vol.193, issue.1, pp.197-208, 1998.
DOI : 10.1007/s002200050324

B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersive media, Dokl. Akad. Nauk SSSR. Translation in Sov. Phys. Dokl, vol.192, pp.753-756, 1970.

A. V. Kazeykina, A large-time asymptotics for the solution of the Cauchy problem for the Novikov???Veselov equation at negative energy with non-singular scattering data, Inverse Problems, vol.28, issue.5, p.55017, 2012.
DOI : 10.1088/0266-5611/28/5/055017

URL : https://hal.archives-ouvertes.fr/hal-00606501

A. V. Kazeykina, Absence of solitons with sufficient algebraic localization for the Novikov-Veselov equation at nonzero energy, Functional Analysis and Its Applications, vol.279, issue.9, p.2012
DOI : 10.1007/s10688-014-0043-2

URL : https://hal.archives-ouvertes.fr/hal-00659483

A. V. Kazeykina, Absence of traveling wave solutions of conductivity type for the Novikov-Veselov equation at zero energy, Funct. Anal. Appl, p.2012

A. V. Kazeykina and R. G. Novikov, A LARGE TIME ASYMPTOTICS FOR TRANSPARENT POTENTIALS FOR THE NOVIKOV???VESELOV EQUATION AT POSITIVE ENERGY, Journal of Nonlinear Mathematical Physics, vol.59, issue.3, pp.377-400, 2011.
DOI : 10.1142/S1402925111001660

URL : https://hal.archives-ouvertes.fr/hal-00526400

A. V. Kazeykina and R. G. Novikov, Absence of exponentially localized solitons for the Novikov???Veselov equation at negative energy, Nonlinearity, vol.24, issue.6, pp.1821-1830, 2011.
DOI : 10.1088/0951-7715/24/6/007

URL : https://hal.archives-ouvertes.fr/hal-00562533

A. V. Kazeykina and R. G. Novikov, Large time asymptotics for the Grinevich???Zakharov potentials, Bulletin des Sciences Math??matiques, vol.135, issue.4, pp.374-382, 2011.
DOI : 10.1016/j.bulsci.2011.02.003

URL : https://hal.archives-ouvertes.fr/hal-00536791

O. M. Kiselev, Asymptotics of a solution of the Kadomtsev?Petviashvili?2 equation, Proc. Inst. Math. Mech, pp.105-134, 2001.

B. Konopelchenko and A. Moro, Integrable Equations in Nonlinear Geometrical Optics, Studies in Applied Mathematics, vol.113, issue.4, pp.325-352, 2004.
DOI : 10.1111/j.0022-2526.2004.01536.x

M. Lassas, J. L. Mueller, and S. Siltanen, Mapping Properties of the Nonlinear Fourier Transform in Dimension Two, Communications in Partial Differential Equations, vol.30, issue.4, pp.591-610, 2007.
DOI : 10.1088/0266-5611/10/6/015

M. Lassas, J. L. Mueller, S. Siltanen, and A. Stahel, The Novikov???Veselov equation and the inverse scattering method, Part I: Analysis, Physica D: Nonlinear Phenomena, vol.241, issue.16, pp.1322-1335, 2012.
DOI : 10.1016/j.physd.2012.04.010

P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, vol.15, issue.5, pp.467-490, 1968.
DOI : 10.1002/cpa.3160210503

S. V. Manakov, The inverse scattering method and two-dimensional evolution equations, Uspekhi Mat. Nauk, vol.31, issue.5, pp.245-246, 1976.

S. V. Manakov, P. M. Santini, and L. A. Takchtadzyan, An asymptotic behavior of the solutions of the Kadomtsev-Petviashvili equations, Phys. Lett. A, pp.75-451, 1988.

S. V. Manakov, V. E. Zakharov, L. A. Bordag, A. R. Its, and V. Matveev, Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction, Physics Letters A, vol.63, issue.3, pp.205-206, 1977.
DOI : 10.1016/0375-9601(77)90875-1

A. I. Nachman, Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem, The Annals of Mathematics, vol.143, issue.1, pp.71-96, 1995.
DOI : 10.2307/2118653

R. G. Novikov, Reconstruction of a two-dimensional Schrödinger operator from the scattering amplitude at fixed energy, Funkt. Anal. i Pril. Translation in Funkt. Anal. and Appl, vol.20, issue.20, pp.90-91, 1986.

R. G. Novikov, Multidimensional inverse spectral problem for the equation ??? + (v(x) ? Eu(x))? = 0, Functional Analysis and Its Applications, vol.38, issue.3, pp.11-22, 1988.
DOI : 10.1007/BF01077418

R. G. Novikov, The inverse scattering problem on a fixed energy level for the two-dimensional Schr??dinger operator, Journal of Functional Analysis, vol.103, issue.2, pp.409-463, 1992.
DOI : 10.1016/0022-1236(92)90127-5

R. G. Novikov, Approximate solution of the inverse problem of quantum scattering theory with fixed energy in dimension 2, Proc. Steklov Inst. Math, pp.301-318, 1999.

R. G. Novikov, Absence of exponentially localized solitons for the Novikov???Veselov equation at positive energy, Physics Letters A, vol.375, issue.9, pp.1233-1235, 2011.
DOI : 10.1016/j.physleta.2011.01.052

URL : https://hal.archives-ouvertes.fr/hal-00523343

S. P. Novikov, S. V. Manakov, L. Pitaevskii, and V. E. Zakharov, Theory of solitons. The inverse scattering method, Contemporary Soviet Mathematics (Transl. from Russian), 1984.

S. P. Novikov and A. P. Veselov, Finite-zone, two-dimensional, potential Schrödinger operators. Explicit formula and evolutions equations, Dokl. Akad. Nauk SSSR Translation in Sov. Math. Dokl, vol.279, pp.20-24, 1984.

S. P. Novikov and A. P. Veselov, Finite-zone, two-dimensional, potential Schrödinger operators. Potential operators, Dokl. Akad. Nauk SSSR Translation in Sov. Math. Dokl, vol.279, pp.784-788, 1984.

P. A. Perry, Miura maps and inverse scattering for the Novikov???Veselov equation, Analysis & PDE, vol.7, issue.2, 2012.
DOI : 10.2140/apde.2014.7.311

T. Regge, Introduction to complex orbital momenta, Il Nuovo Cimento, vol.10, issue.5, pp.951-976, 1959.
DOI : 10.1007/BF02728177

M. Santacesaria, Uniqeness, reconstruction, stability for the two-dimensional inverse problems, 2012.

H. Segur, The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1, Journal of Fluid Mechanics, vol.19, issue.04, pp.721-736, 1973.
DOI : 10.1103/PhysRevLett.19.1095

I. A. Taimanov and S. P. Tsarev, On the Moutard transformation and its applications to spectral theory and Soliton equations, Journal of Mathematical Sciences, vol.31, issue.3, pp.371-387, 2010.
DOI : 10.1007/s10958-010-0092-x

T. Tsai, The Schrodinger operator in the plane, Inverse Problems, vol.9, issue.6, pp.763-787, 1993.
DOI : 10.1088/0266-5611/9/6/012

A. Vasy, W. , and X. , Inverse scattering with fixed energy for dilation-analytic potentials, Inverse Problems, vol.20, issue.4, pp.1349-1354, 2004.
DOI : 10.1088/0266-5611/20/4/020

I. N. Vekua, Generalized analytic functions, 1962.

R. Weder, Y. , and D. , On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity. Inverse Problems, pp.1937-1952, 2005.

V. E. Zakharov and E. A. Kuznetsov, Three-dimensional solitons, JETP Translation in Sov. Phys. JETP, vol.66, issue.392, pp.594-597, 1974.

V. E. Zakharov and S. V. Manakov, Asymptotic behaviour of non-linear wave systems integrated by the inverse scattering method, JETP Translation in Sov. Phys. JETP, vol.71, issue.441, pp.203-215, 1976.