V. A. Arkad-'ev, A. K. Pogrebkov, and M. K. Polivanov, Singular solutions of the KdV equation and the inverse scattering method, Journal of Soviet Mathematics, issue.6, pp.31-3264, 1985.

R. Beals and R. R. Coifman, The spectral problem for the Davey-Stewartson and Ishimori hierarchies Nonlinear evolution equations: integrability and spectral methods, Proc. Workshop, pp.15-23, 1988.

L. Bers, Theory of pseudo-analytic functions, Institute for Mathematics and Mechanics, p.187, 1953.

M. M. Crum, ASSOCIATED STURM-LIOUVILLE SYSTEMS, The Quarterly Journal of Mathematics, vol.6, issue.1, pp.121-127, 1955.
DOI : 10.1093/qmath/6.1.121

A. Doliwa, P. Grinevich, M. Nieszporski, and P. M. Santini, Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme, Journal of Mathematical Physics, vol.48, issue.1, p.13513, 2007.
DOI : 10.1063/1.2406056

J. J. Duistermaat and F. A. Grünbaum, Differential equations in the spectral parameter, Communications in Mathematical Physics, vol.4, issue.4, pp.177-240, 1986.
DOI : 10.1007/BF01206937

L. D. Faddeev, Inverse problem of quantum scattering theory. II., Journal of Soviet Mathematics, vol.107, issue.No. 1, pp.334-396, 1976.
DOI : 10.1007/BF01083780

A. S. Fokas and L. Sung, On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations, Inverse Problems, vol.8, issue.5, pp.673-708, 1992.
DOI : 10.1088/0266-5611/8/5/002

P. G. Grinevich, The scattering transform for the two-dimensional Schrödinger operator with a potential that decreases at infinity at fixed nonzero energy, pp.1015-1083, 2000.

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.1102-1106, 2012.
DOI : 10.1016/j.physleta.2012.02.025

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

P. G. Grinevich and R. G. Novikov, Faddeev eigenfunctions for multipoint potentials, Eurasian Journal of Mathematical and Computer Applications, vol.1, issue.2, pp.76-91, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00747888

P. G. Grinevich and R. G. Novikov, Moutard Transform for Generalized Analytic Functions, The Journal of Geometric Analysis, vol.97, issue.1
DOI : 10.1007/s12220-015-9657-8

URL : https://hal.archives-ouvertes.fr/hal-01222481

P. G. Grinevich and R. G. Novikov, Generalized analytic functions, Moutard-type transforms, and holomorphic maps, Functional Analysis and Its Applications, vol.97, issue.1
DOI : 10.1007/s10688-016-0140-5

URL : https://hal.archives-ouvertes.fr/hal-01234004

P. G. Grinevich and S. P. Novikov, Two-dimensional " inverse scattering problem " for negative energies and generalized-analytic functions. 1. Energies below the ground state, Functional Analysis and Its Applications, pp.19-27, 1988.

P. G. Grinevich and S. P. Novikov, Singular soliton operators and indefinite metrics, Bulletin of the Brazilian Mathematical Society, New Series, vol.3, issue.1, pp.809-840, 2013.
DOI : 10.1007/s00574-013-0035-5

P. G. Grinevich and S. P. Novikov, Spectrally meromorphic operators and non-linear systems, Russian Mathematical Surveys, vol.69, issue.5, pp.924-926, 2014.
DOI : 10.1070/RM2014v069n05ABEH004922

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

G. M. Henkin and R. G. Novikov, The ¯ ?-equation in the multidimensional inverse scattering problem, Russian Math. Surveys, vol.42, issue.3, pp.109-180, 1987.

E. L. Lakshtanov, R. G. Novikov, and B. R. Vainberg, A global Riemann- Hilbert problem for two-dimensional inverse scattering at fixed energy
URL : https://hal.archives-ouvertes.fr/hal-01203044

V. B. Matveev and M. A. Salle, Darboux transformations and solitons, Springer Series in Nonlinear Dynamics, 1991.

T. F. Moutard, Sur la construction deséquationsdeséquations de la forme 1 z ? 2 z ?x?y = ?(x, y) qui admettenent une intégrale générale explicite, J. ´ Ecole Polytechnique, pp.45-46, 1878.

J. J. Nimmo and W. K. Schief, Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)-dimensional sine-Gordon system, Proc. R. Soc. London A, pp.453-255, 1997.
DOI : 10.1098/rspa.1997.0015

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 and I. A. Taimanov, The Moutard transformation and two-dimensional multipoint delta-type potentials, Russian Mathematical Surveys, vol.68, issue.5, pp.957-959, 2013.
DOI : 10.1070/RM2013v068n05ABEH004864

URL : https://hal.archives-ouvertes.fr/hal-00846512

R. G. Novikov, I. A. Taimanov, and S. P. Tsarev, Two-dimensional von Neumann-Wigner potentials with a multiple positive eigenvalue, Functional Analysis and Its Applications, pp.295-297, 2014.

I. A. Taimanov, Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces, Theoretical and Mathematical Physics, vol.363, issue.2, pp.173-181, 2015.
DOI : 10.1007/s11232-015-0255-5

I. A. Taimanov, The Moutard transformation of two-dimensional Dirac operators and M??bius geometry, Mathematical Notes, vol.97, issue.1-2, pp.124-135, 2015.
DOI : 10.1134/S0001434615010149

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

I. N. Vekua, Generalized Analytic Functions, 1962.