M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Nonlinear evolution equation of physical signicance, Phys. Rev. Lett, vol.31, p.125127, 1973.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems, Studies in Applied Mathematics, vol.34, issue.12, p.249, 1974.
DOI : 10.1002/sapm1974534249

M. J. Ablowitz, B. Prinari, and A. D. Trubatch, Integrable Nonlinear Schrödinger Systems and their Soliton Dynamics, Dynamics of PDE, vol.1, issue.3, p.239299, 2004.
DOI : 10.4310/dpde.2004.v1.n3.a1

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, First-order exact solutions of the nonlinear Schrödinger equation, Teoret. Mat. Fiz, vol.72, issue.2, p.183196809818, 1987.

N. Akhmediev, J. Soto-crespo, and A. Ankiewicz, Extreme waves that appear from nowhere: On the nature of rogue waves, Physics Letters A, vol.373, issue.25, p.21372145, 2009.
DOI : 10.1016/j.physleta.2009.04.023

M. S. Alber, N-component integrable systems and geometric asymptotics, In Integrability: The Seiberg-Witten and Whitham equations

M. S. Alber, R. Camassa, F. Fedorov, D. D. Holm, and J. E. Marsden, On billiard solutions of nonlinear PDE's, Phys. Lett. A, vol.264, p.171178, 1999.

M. S. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, The geometry of peaked solitons and billiard solutions of a class of integrable PDE's, Letters in Mathematical Physics, vol.64, issue.2, p.137151, 1994.
DOI : 10.1007/BF00739423

M. S. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, On the link between umbilic geodesics and soliton solutions of nonlinear PDE's, Proc, Roy. Soc, vol.450, p.677692, 1995.

M. S. Alber, R. Camassa, F. Fedorov, N. Yu, D. D. Holm et al., On billiard solutions of nonlinear PDE's, Phys. Lett. A, vol.264, p.171178, 1999.

M. S. Alber, R. Camassa, F. Fedorov, N. Yu, D. D. Holm et al., The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's??of Shallow Water and Dym Type, Communications in Mathematical Physics, vol.221, issue.1, p.197227, 2001.
DOI : 10.1007/PL00005573

M. S. Alber, F. Fedorov, and N. Yu, Wave solutions of evolution equations and Hamiltonian ows on nonlinear subvarieties of generalized Jacobians, J. Phys. A, vol.33, p.84098425, 2000.

M. S. Alber, F. Fedorov, and N. Yu, Algebraic geometrical solutions for certain evolution equations and Hamiltonian ows on nonlinear subvarieties of generalized Jacobians, Inverse Problems, vol.17, p.10171042, 2001.

N. Andonowati, E. Karjanto, and . Van-groesen, Extreme wave phenomena in down-stream running modulated waves, Applied Mathematical Modelling, vol.31, issue.7, p.14251443, 2007.
DOI : 10.1016/j.apm.2006.04.015

D. Anker and N. C. Freeman, On the Soliton Solutions of the Davey-Stewartson Equation for Long Waves, Proc. R. Soc. London A 360, p.529, 1978.
DOI : 10.1098/rspa.1978.0083

E. Arbarello, Fay???s trisecant formula and a characterization of Jacobian varieties, Proceedings of Symposia in Pure Mathematics, 1987.
DOI : 10.1090/pspum/046.1/927948

V. A. Arkadiev, A. K. Pogrebkov, and M. C. Polivanov, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Physica D: Nonlinear Phenomena, vol.36, issue.1-2, p.189197, 1989.
DOI : 10.1016/0167-2789(89)90258-3

V. I. Arnold, Mathematical methods of classical mechanics of Graduate Texts in Mathematics Translated from the 1974 Russian original by K. Vogtmann and A, 1989.

W. Beals, D. Sattinger, and J. Szmigielski, Acoustic Scattering and the Extended Korteweg??? de Vries Hierarchy, Advances in Mathematics, vol.140, issue.2, p.190206, 1998.
DOI : 10.1006/aima.1998.1768

URL : http://doi.org/10.1006/aima.1998.1768

W. Beals, D. Sattinger, and J. Szmigielski, Multi-peakons and a theorem of Stieltjes, Inverse Problems, vol.15, issue.1, pp.1-4, 1999.
DOI : 10.1088/0266-5611/15/1/001

W. Beals, D. Sattinger, and J. Szmigielski, Multipeakons and the classical moment, Adv. in Math, vol.154, issue.2, p.229257, 2000.

E. Belokolos, A. Bobenko, V. Enolskii, A. Its, and V. Matveev, Algebro-geometric approach to nonlinear integrable equations, Series in nonlinear dynamics, 1994.

L. A. Bordag and A. I. Bobenko, Periodic Multiphase Solutions of the Kadomtsev-Petviashviliequation, J. Phys. A: Math. and General, vol.22, p.1259, 1989.

M. Boiti, J. Leon, L. Martina, and F. Pempineili, Scattering of localized solitons in the plane, Physics Letters A, vol.132, issue.8-9, p.432439, 1988.
DOI : 10.1016/0375-9601(88)90508-7

M. Boiti, L. Martina, and F. Pempinelli, Multidimensional localized solitons, Chaos, Solitons & Fractals, vol.5, issue.12, p.23772417, 1995.
DOI : 10.1016/0960-0779(94)E0106-Y

URL : http://arxiv.org/abs/patt-sol/9311002

F. Calogero, An integrable Hamiltonian system, Physics Letters A, vol.201, issue.4, p.306310, 1995.
DOI : 10.1016/0375-9601(95)00238-X

F. Calogero and J. P. Françoise, Solvable quantum version of an integrable Hamiltonian system, Journal of Mathematical Physics, vol.37, issue.9, p.28632871, 1996.
DOI : 10.1063/1.531653

R. Camassa, CHARACTERISTIC VARIABLES FOR A COMPLETELY INTEGRABLE SHALLOW WATER EQUATION, Nonlinearity, Integrability and All That: Twenty Years After NEEDS'79, 2000.
DOI : 10.1142/9789812817587_0009

R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Physical Review Letters, vol.71, issue.11, p.16611664, 1993.
DOI : 10.1103/PhysRevLett.71.1661

R. Camassa, D. D. Holm, and J. M. Hyman, A New Integrable Shallow Water Equation, Adv. Appl. Mech, vol.31, p.133, 1994.
DOI : 10.1016/S0065-2156(08)70254-0

D. Y. Chen, Introduction to Solitons, 2006.

I. V. Cherednik, Reality conditions in nite-zone integration English translation: Sov, Dokl. Akad. Nauk SSSR Phys. Dokl, vol.25, issue.25, pp.11041108-450452, 1980.

A. Clebsch, Zur Theorie der binären Formen sechster Ordnung und zur Dreitheilung der hyperelliptischen Funktionen, Abh. der k, Ges. Wiss. zu Göttingen, vol.14, p.159, 1869.
DOI : 10.1007/bf01444019

E. Date and S. Tanaka, Analogue of Inverse Scattering Theory for the Discrete Hill's Equation and Exact Solutions for the Periodic Toda Lattice, Progress of Theoretical Physics, vol.55, issue.2, p.457465, 1976.
DOI : 10.1143/PTP.55.457

A. Davey and K. Stewartson, On Three-Dimensional Packets of Surface Waves, Proc. R. Soc. Lond. A 388, p.101110, 1974.
DOI : 10.1098/rspa.1974.0076

B. Deconinck and M. Van-hoeij, Computing Riemann matrices of algebraic curves, Physica D: Nonlinear Phenomena, vol.152, issue.153, p.152153, 2001.
DOI : 10.1016/S0167-2789(01)00156-7

B. Deconinck and M. Patterson, Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package ???Algcurves???, Computational Approach to Riemann Surfaces, Lect. Notes Math, p.2013, 2011.
DOI : 10.1007/978-3-642-17413-1_2

L. A. Dmitrieva, Finite-gap solutions of the Harry Dym equation, Physics Letters A, vol.182, issue.1, 1993.
DOI : 10.1016/0375-9601(93)90054-4

L. A. Dmitrieva, The higher-times approach to multisoliton solutions of the Harry Dym equation, Journal of Physics A: Mathematical and General, vol.26, issue.21, p.60056020, 1993.
DOI : 10.1088/0305-4470/26/21/037

O. Dolgopolova and E. Zverovich, Explicit construction of global uniformization of an algebraic correspondence (Russian), ii, p.6173, 2000.

P. Dubard, P. Gaillard, C. Klein, and V. B. Matveev, On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation, The European Physical Journal Special Topics, vol.25, issue.1, p.258, 2010.
DOI : 10.1140/epjst/e2010-01252-9

B. A. Dubrovin, Matrix nite-zone operators, Revs. Sci. Tech, vol.23, p.2050, 1983.
DOI : 10.1007/bf02104895

B. A. Dubrovin, Theta functions and non-linear equationsEnglish translation: Russ, Usp. Mat. Nauk Math. Surv, vol.36, issue.36 2, pp.1180-1192, 1981.
DOI : 10.1070/rm1981v036n02abeh002596

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.474.2549

B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, Integrable systems, Dynamical systems 4, Itogi Nauki i Tekhniki Nauk SSSR, 1985.

B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Nonlinear equations of Korteweg-de Vries type, nite-zone linear operators, and Abelian varieties, Russian mathematical surveys 31, p.59146, 1976.

B. A. Dubrovin and S. Natanzon, REAL THETA-FUNCTION SOLUTIONS OF THE KADOMTSEV???PETVIASHVILI EQUATION, Mathematics of the USSR-Izvestiya, vol.32, issue.2, p.269288, 1989.
DOI : 10.1070/IM1989v032n02ABEH000759

S. N. Eilenberger, An Introduction to Dierence Equations, 1996.

D. Eisenbud, N. Elkies, J. Harris, and R. Speiser, On the Hurwitz scheme and its monodromy, Compositio Mathematica, vol.77, issue.1, p.95117, 1991.

V. Eleonskii, I. Krichever, and N. Kulagin, Rational multisoliton solutions to the NLS equation, Soviet Doklady 1986 sect, Math. Phys, vol.287, p.606610, 1986.

J. Elgin, V. Enolski, and A. Its, Eective integration of the nonlinear vector Schrödinger equation, Physica D, vol.22522, p.127152, 2007.

B. Eynard, A. Kokotov, and D. , Genus one contribution to free energy in Hermitian two-matrix model, Nuclear Physics B, vol.694, issue.3, p.443, 2004.
DOI : 10.1016/j.nuclphysb.2004.06.031

L. Faddeev and L. Takhtajan, Hamiltonian Methods in the Theory of Solitons, 1987.
DOI : 10.1007/978-3-540-69969-9

H. M. Farkas and I. Kra, Riemann surfaces, Graduate Texts in Mathematics, vol.71, 1980.

H. M. Farkas, On Fay's trisecant formula, J. Analyse Math, vol.44, 1984.

J. Fay, Theta functions on Riemann surfaces, Lecture Notes in Mathematics, vol.352, 1973.
DOI : 10.1007/BFb0060090

H. Flaschka, The Toda lattice, Phys. Rev, vol.9, 1924.

A. S. Fokas and B. Fuchssteiner, Symplectic structures, their Bäcklund transformations and hereditary symmetries, Physica D, vol.482, p.4766, 1981.

A. S. Fokas and P. M. Santini, Dromions and a boundary value problem for the Davey-Stewartson 1 equation, Physica D: Nonlinear Phenomena, vol.44, issue.1-2, p.99, 1990.
DOI : 10.1016/0167-2789(90)90050-Y

P. J. Forrester, N. C. Snaith, and J. J. Verbaarshot, Developments in random matrix theory, Journal of Physics A: Mathematical and General, vol.36, issue.12, p.1, 2003.
DOI : 10.1088/0305-4470/36/12/201

J. Frauendiener and C. Klein, Hyperelliptic theta-functions and spectral methods, Journal of Computational and Applied Mathematics, vol.167, issue.1, 2004.
DOI : 10.1016/j.cam.2003.10.003

J. Frauendiener and C. Klein, Hyperelliptic Theta-Functions and Spectral Methods: KdV and KP Solutions, Letters in Mathematical Physics, vol.33, issue.2, p.249267, 2006.
DOI : 10.1007/s11005-006-0068-4

URL : http://arxiv.org/abs/nlin/0512066

J. Frauendiener and C. Klein, Algebraic Curves and Riemann Surfaces in Matlab, Riemann Surfaces Computational Approaches, p.2013, 2011.
DOI : 10.1007/978-3-642-17413-1_3

N. C. Freeman, Soliton Solutions of Non-linear Evolution Equations, IMA Journal of Applied Mathematics, vol.32, issue.1-3, p.125, 1984.
DOI : 10.1093/imamat/32.1-3.125

N. C. Freeman and J. J. Nimmo, Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique, Physics Letters A, vol.95, issue.1, p.1, 1983.
DOI : 10.1016/0375-9601(83)90764-8

C. S. Gardner, J. M. Greene, R. Miura, and M. , Korteweg-devries equation and generalizations. VI. methods for exact solution, Method for Solving the Korteweg-de Vries Equation, p.97, 1974.
DOI : 10.1002/cpa.3160270108

F. Gesztesy and H. Holden, Soliton Equations and Their Algebro-Geometric Solutions, Volume I: (1+1)-Dimensional Continuous Models, Cambridge studies in advanced mathematics, 2003.

B. H. Gross and J. Harris, Real algebraic curves, Annales scientifiques de l'??cole normale sup??rieure, vol.14, issue.2, p.157182, 1981.
DOI : 10.24033/asens.1401

R. C. Gunning, Some Identities for Abelian Integrals, American Journal of Mathematics, vol.108, issue.1, 1985.
DOI : 10.2307/2374468

A. Harnack, Ueber die Vieltheiligkeit der ebenen algebraischen Curven, Mathematische Annalen, vol.10, issue.2, p.189199, 1876.
DOI : 10.1007/BF01442458

K. L. Henderson, D. H. Peregrine, and J. W. Dold, Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schr??dinger equation, Wave Motion, vol.29, issue.4, p.341361, 1999.
DOI : 10.1016/S0165-2125(98)00045-6

R. Hirota, Korteweg-de Vries Equation for Multiple Collisions of Solitons, Journal of the Physical Society of Japan, vol.33, issue.5, p.1192, 1971.
DOI : 10.1143/JPSJ.33.1456

J. K. Hunter and Y. X. Zheng, On a completely integrable nonlinear hyperbolic variational equation, Physica D: Nonlinear Phenomena, vol.79, issue.2-4, pp.79-36186, 1994.
DOI : 10.1016/S0167-2789(05)80015-6

A. R. Its, Inversion of hyperelliptic integrals and integration of nonlinear dierential equations, Vestn. Leningr. Gos. Univ, vol.7, issue.2, p.3746, 1976.

A. R. Its and V. P. Kotlyarov, Explicit formulas for solutions of the Nonlinear Schrödinger equation, Dokl. Akad. Nauk Ukrain. SSR, Ser. A, issue.11, p.965968, 1976.

A. Its and V. Matveev, Schrödinger operators with the nite-band spectrum and the N-soliton solutions of the Korteweg-de Vries equation, Russian) Teoret. Mat. Fiz, vol.23, issue.1, p.5168, 1975.

A. R. Its, A. V. Rybin, and M. A. Salle, Exact integration of nonlinear Schrödinger equation, Teore. i Mat. Fiz, vol.74, issue.1, p.2945, 1988.

C. G. Jacobi, Crelle's Journ. f. Math, p.394, 1832.

M. Kac and P. Van-moerbeke, A complete solution of the periodic Toda problem, Proceedings of the National Academy of Sciences, vol.72, issue.8, p.72, 1975.
DOI : 10.1073/pnas.72.8.2879

C. Kalla, New degeneration of Fay's identity and its application to integrable systems, preprint arXiv, pp.1104-2568, 2011.

C. Kalla, Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions, J. Phys. A : Math. Theor, p.44, 2011.

C. Kalla and C. Klein, On the numerical evaluation of algebro-geometric solutions to integrable equations, Nonlinearity, vol.25, issue.3, p.601630, 2011.
DOI : 10.1088/0951-7715/25/3/569

URL : https://hal.archives-ouvertes.fr/hal-00601630

T. Kanna, M. Lakshmanan, P. Tchofo-dinda, and N. Akhmediev, Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrödinger equations, Phys. Rev. E, vol.73, 2006.

C. Klein, D. Korotkin, and V. Shramchenko, Ernst equation, Fay identities and variational formulas on hyperelliptic curves, Mathematical Research Letters, vol.9, issue.1, p.120, 2002.
DOI : 10.4310/MRL.2002.v9.n1.a3

URL : http://arxiv.org/abs/math-ph/0401055

C. Klein and O. Richter, Ernst Equation and Riemann Surfaces, Lecture Notes in Physics, vol.685, 2005.

D. Korotkin, Finite-gap solutions of the stationary axisymmetric Einstein equation in vacuum, Theoretical and Mathematical Physics, vol.70, issue.1, p.10181031, 1989.
DOI : 10.1007/BF01028676

D. Korotkin and V. Shramchenko, Riemann???Hilbert Problems for Hurwitz Frobenius Manifolds, Letters in Mathematical Physics, vol.144, issue.1, p.543, 2009.
DOI : 10.1007/s11005-010-0435-z

V. A. Kozel and V. P. Kotlyarov, Almost periodic solutions of the equation u tt ? u xx + sin(u) = 0, Dokl. Akad. Nauk Ukrain. SSR Ser. A no, vol.10, p.878881, 1976.

I. M. Krichever, Algebro-geometric construction of the Zakharov-Shabat equations and their periodic solutions, Sov. Math. Dokl, vol.17, p.394397, 1976.

I. M. Krichever, Integration of nonlinear equations by the methods of algebraic geometry, Funkts, Anal. Prilozh. Funct. Anal. Appl, vol.11, issue.11, pp.1531-1226, 1977.

I. M. Krichever, METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS, English translation, pp.183208-185213, 1977.
DOI : 10.1070/RM1977v032n06ABEH003862

I. M. Krichever, Algebraic curves and nonlinear dierence equations, Russian Math. Surveys, vol.334, p.255256, 1978.

I. M. Krichever, Nonlinear equations and elliptic curves, Journal of Soviet Mathematics, vol.45, issue.2, p.5190, 1983.
DOI : 10.1007/BF02104896

I. M. Krichever, Algebro-geometric spectral theory of the Schrödinger dierence operator and the Peierls model, Soviet Math. Dokl, vol.26, p.194198, 1982.

I. M. Krichever, The peierls model, Functional Analysis and Its Applications, vol.9, issue.1, p.248263, 1982.
DOI : 10.1007/BF01077847

I. M. Krichever, The averaging method for two-dimensional integrable equations, (Russian) Funktsional. Anal. i Prilozhen); translation in Funct, Anal. Appl, vol.22, issue.22 3, pp.96-200213, 1988.

I. M. Krichever, Algebraic-geometrical methods in the theory of integrable equations and their perturbations, Acta Appl. Math, vol.39, p.93125, 1995.

I. M. Krichever and S. P. Novikov, Holomorphic bundles over Riemann surfaces and the Kadomtsev-Petviashvili (KP) equation. I, Funkts, English translation, p.276286, 1978.

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

P. D. Lax, Periodic solutions of the KdV equation, Communications on Pure and Applied Mathematics, vol.15, issue.3, p.141188, 1975.
DOI : 10.1002/cpa.3160280105

Y. C. Ma, The perturbed plane-wave solutions of the cubic Schrödinger equation, Stud. Appl. Math, vol.60, issue.1, p.4358, 1979.

S. V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, Sov. Phys, JETP, vol.38, p.248, 1974.

S. V. Manakov, Complete integrability and stochastization of discrete dynamical systems, Soviet Phys, JETP, vol.40, p.269274, 1974.

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

T. Malanyuk, Finite-gap solutions of the Davey-Stewartson equations, Journal of Nonlinear Science, vol.18, issue.1, p.121, 1994.
DOI : 10.1007/BF02430624

Y. Matsuno, Multiperiodic and multisoliton solutions of a nonlocal nonlinear Schr??dinger equation for envelope waves, Physics Letters A, vol.278, issue.1-2, p.53, 2000.
DOI : 10.1016/S0375-9601(00)00757-X

V. B. Matveev and M. A. Salli, Darboux Transformations and Solitons, Springer Series in Nonlinear Dynamics, 1991.

M. Mcconnell, A. Fokas, and B. Pelloni, Localized coherent solutions of the DSI and DSII equationsa numerical study, Mathematics and Computers in Simulation, vol.69, issue.424, pp.5-6, 2005.

S. Mccullough, The trisecant identity and operator theory, Integral Equations Operator Theory, p.104128, 1996.

H. P. Mckean and A. Constantin, A shallow water equation on the circle, Comm. Pure Appl. Math, vol.LII, p.949982, 1999.

H. P. Mckean and P. Van-moerbeke, The spectrum of Hill's equation, Inventiones Math, p.217274, 1975.

P. Van-moerbeke and D. Mumford, The spectrum of dierence operators and algebraic curves, Acta Math, p.97154, 1979.

D. Mumford, An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related non-linear equations, Intl. Symp. Algebraic Geometry, vol.115153, p.Kyoto, 1977.

D. Mumford, Tata Lectures on Theta. I and II., Progress in Mathematics 28 and 43, respectively, 1983.

J. J. Nimmo and N. C. Freeman, The use of Backlund transformations in obtaining N-soliton solutions in Wronskian form, Journal of Physics A: Mathematical and General, vol.17, issue.7, p.1415, 1984.
DOI : 10.1088/0305-4470/17/7/009

S. P. Novikov, The periodic problem for the Korteweg-de Vries equation, p.5466, 1974.

D. P. Novikov, Algebraic-geometrical solutions of the HarryDym equations, Sibirskii Matematicheskii Zhurnal 40, 159163, (Russian) English transl. in: Siberian Math, Journal, vol.40, p.136140, 1999.

S. Novikov, S. Manakov, L. Pitaevskii, and V. Zakharov, Theory of Solitons -The Inverse Scattering Method, 1980.

A. R. Osborne, M. Onorato, and M. Serio, The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains, Physics Letters A, vol.275, issue.5-6, p.386393, 2000.
DOI : 10.1016/S0375-9601(00)00575-2

R. S. Palais, The symmetries of solitons, Bulletin of the American Mathematical Society, vol.34, issue.04, p.339403, 1997.
DOI : 10.1090/S0273-0979-97-00732-5

D. H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions, J. Austral . Math. Soc. Ser. B, vol.25, issue.1, p.1643, 1983.

A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Dierential Equations, 2004.

C. Poor, Fay's trisecant formula and cross-ratios, 1992.
DOI : 10.2307/2159386

E. Previato, Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation, Duke Math, J, vol.52, p.329377, 1985.

R. Radhakrishnan and M. Lakshmanan, Bright and dark soliton solutions to coupled nonlinear Schrödinger equations, J. Phys. A, Math. Gen, vol.28, p.26832692, 1995.
DOI : 10.1088/0305-4470/28/9/025

R. Radhakrishnan and M. Lakshmanan, Inelastic collision and switching of coupled bright solitons in optical fibers, Physical Review E, vol.56, issue.2, p.2213, 1997.
DOI : 10.1103/PhysRevE.56.2213

R. Radha and M. Lakshmanan, Localized coherent structures and integrability in a generalized (2 + 1)-dimensional nonlinear Schr??dinger equation, Chaos, Solitons & Fractals, vol.8, issue.1, p.17, 1997.
DOI : 10.1016/S0960-0779(96)00090-2

R. Radhakrishnan, R. Sahadevan, and M. Lakshmanan, Integrability and singularity structure of coupled nonlinear Schr??dinger equations, Chaos, Solitons & Fractals, vol.5, issue.12, pp.2315-2327, 1995.
DOI : 10.1016/0960-0779(94)E0101-T

A. Raina, Fay's trisecant identity and conformal field theory, Communications in Mathematical Physics, vol.178, issue.153, p.625, 1989.
DOI : 10.1007/BF01256498

URL : http://projecteuclid.org/download/pdf_1/euclid.cmp/1104178594

G. Rosenhain, Crelle's Journ. f, Math, vol.40, p.319, 1850.

J. S. Russell, Report on waves, Proc. Roy. Soc. Edinburgh, p.319320, 1844.

P. M. Santini, Energy exchange of interacting coherent structures in multidimensions, Physica D: Nonlinear Phenomena, vol.41, issue.1, p.2654, 1990.
DOI : 10.1016/0167-2789(90)90026-L

T. Shiota, Characterization of Jacobian varieties in terms of soliton equations, Inventiones Mathematicae, vol.120, issue.6, p.333382, 1986.
DOI : 10.1007/BF01388967

H. Stahl, Theorie der Abel'schen Functionen, 1896.

M. Tajiri and T. Arai, Periodic soliton solutions to the Davey-Stewartson equation, Proc. Inst. Math. Natl. Acad. Sci. Ukr. 30, p.210217, 2000.

M. Toda, Theory of Nonlinear Lattices, 2nd enl, 1989.

M. Toda, Theory of Nonlinear Waves and Solitons, 1989.

L. N. Trefethen, Spectral Methods in Matlab, 2000.
DOI : 10.1137/1.9780898719598

C. L. Tretko and M. D. Tretko, Combinatorial group theory, Riemann surfaces and dierential equations, Contemporary Mathematics, vol.33, p.467517, 1984.

M. Trott, Applying Groebner Basis to Three Problems in Geometry, Mathematica in Education and Research, vol.6, issue.1, p.1528, 1997.

V. Vinnikov, Self-adjoint determinantal representations of real plane curves, Mathematische Annalen, vol.28, issue.1, p.453479, 1993.
DOI : 10.1007/BF01445115

N. Yoshida, K. Nishinari, J. Satsuma, and K. Abe, Dromion can be remote-controlled, Journal of Physics A: Mathematical and General, vol.31, issue.14, p.3325, 1998.
DOI : 10.1088/0305-4470/31/14/017

N. J. Zabusky and M. D. , Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States, Physical Review Letters, vol.15, issue.6, p.240243, 1965.
DOI : 10.1103/PhysRevLett.15.240

V. Zakharov and S. Manakov, On the complete integrability of a nonlinear Schrödinger equation, Teoret. Mat. Fiz, vol.193, p.332343, 1974.

V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and onedimensional self-modulation of waves in nonlinear media, Soy. Phys. JETP, vol.34, p.6269, 1972.

V. E. Zakharov and A. B. Shabat, A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem, I., Funct, Anal. Appl, vol.8, p.226235, 1974.

V. Zakharov and E. Schulman, To the integrability of the system of two coupled nonlinear Schrödinger equations, Physica D, vol.4, p.270274, 1982.