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Physics and mathematics

of nonlinear processes and models

(University "La Sapienza" , Rome, Italy)

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Paolo Maria Santini

Publications

[1] P. M. Santini: "Asymptotic behaviour (in t) of solutions of the boomeron
equation"; Il Nuovo Cimento 47B, 228 (1978).
[2] P. M. Santini: "Asymptotic behaviour (in t) of solutions of the cylindrical
KdV equation. I"; Il Nuovo Cimento 54A. 241 (1979).
[3] P. M. Santini: "Asymptotic behaviour (in t) of solutions of the cylindrical
KdV equation. II"; Il Nuovo Cimento 57A, 387 (1980).
[4] S. V. Manakov, P. M. Santini and L. A. Takhtajan: "Asymptotic behaviour
of the solutions of the Kadomtsev-Petviashvili equation (two dimensional
Korteweg-de Vries equation)."; Phys.Lett.75A, 451 (1980).
[5] L. Martina and P. M. Santini: "Propagation of ion acoustic waves in cold
inhomogeneous plasmas." Lettere al Nuovo Cimento 29, 513 (1980).
[6] P. M. Santini: "On the evolution of two dimensional packets of water waves
over an uneven bottom."; Lettere al Nuovo Cimento 30, 236 (1981).
[7] D. Levi, L. Pilloni and P. M. Santini: "Backlund transformations for nonlinear
evolution equations in 2+1 dimensions."; Phys.Lett. 81A, 419 (1981).
[8] D. Levi, L. Pilloni and P. M. Santini: "Integrable three- dimensional lattices.";
J.Phys. 14A, 1567 (1981).
[9] P. M. Santini, M. J. Ablowitz and A. S. Fokas: "On the limit from
the Intermediate Long Wave equation to the Benjamin-Ono equation.";
J.Math.Phys. 25, 892 (1984).
[10] A. Degasperis and P. M. Santini: "Linear operator and conservation laws
for a class of nonlinear integro-differential evolution equations."; Phys.Lett.
98A, 240 (1983).
[11] P. M. Santini, M. J. Ablowitz and A. S. Fokas: "The direct linearization of
a class of nonlinear evolution equations."; J.Math.Phys. 25, 2614 (1984).
[12] A. Degasperis, P. M. Santini and M. J. Ablowitz: "Nonlinear evolution
equations associated with a Riemann-Hilbert scattering problem.";
J.Math.Phys. 26, 2469 (1985).
[13] P. M. Santini, M. J. Ablowitz and A. S. Fokas: "On the initial value problem
for a class of nonlinear integral evolution equations including the sine-
Hilbert equation."; J.Math.Phys. 28, 2310 (1987).
[14] O. Ragnisco, P. M. Santini, S. C. Briggs and M. J. Ablowitz: "An example
of DBAR problem arising in a finite difference context: direct and inverse problem
for the discrete analogue of the equation psi_xx+u psi = psi_y"; J.Math.Phys.
28, 777 (1987).
[15] P. M. Santini: "Nonlinear integral evolution equations associated with a
Riemann- Hilbert scattering problem. Aspects of the initial value problem
for the sine-Hilbert class."; in "Systemes Dynamiques non lineaires: integrabilite'
et comportment qualitatif", edited by P.Winternitz, Proceedings
of the Seminaire de Mathematiques Superieures; Les press de l'Universite'
de Montreal, Montreal, 1986.
[16] A. S. Fokas and P. M. Santini: "The recursion operator of the Kadomtsev-
Petviashvili equation and the squared eigenfunctions of the Schroedinger
operator."; Stud.Appl.Math. 75, 179 (1986).
[17] P. M. Santini and A. S. Fokas: "Recursion operators and bi- hamiltonian
structures in multidimensions.I."; Comm.Math.Phys. 115, 375-419 (1988).
[18] A. S. Fokas and P. M. Santini: "Recursion operators and bi- hamiltonian
structures in multidimensions.II."; Comm.Math.Phys. 116, 449-474 (1988).
[19] P. M. Santini and A. S. Fokas: "Symmetries and bi-hamiltonian structures
of 2+1 dimensional systems."; in Topics in Soliton Theory and Exactly
Solvable Nonlinear Equations, edited by M.Ablowitz,B.Fuchssteiner
and M.Kruskal, World Scientific, Singapore, 1987.
[20] P. M. Santini: "Integrable 2+1 dimensional equations, their recursion operators
and bi- hamiltonian structures as reduction of multidimensional
systems"; in Inverse Problems: an Interdisciplinary Study; Supplement 19
of Advances in Electronics and Electron Physics, edited by P.C.Sabatier,
Academic Press; London, New York, Tokyo, 1987.
[21] A. S. Fokas and P. M. Santini: "Integrable equations in multidimensions
(2+1) are bi- hamiltonian systems"; in Solitons, Introduction and
Applications; Proceedings of the Winter School, Bharathidasan University,
Tiruchirapalli, South India, 1987; edited by M.Lakshmanan, Springer-
Verlag; Berlin, Heidelberg, New York, Tokyo, 1988.
[22] O. Ragnisco and P. M. Santini: "Recursion operator and bi- hamiltonian
structure for integrable multidimensional lattices."; J.Math.Phys. 29, 1593
(1988).
[23] A. S. Fokas and P. M. Santini: "Bi-hamiltonian formulation of the
Kadomtsev- Petviashvili and Benjamin-Ono equations."; J.Math.Phys. 29,
604 (1988).
[24] P. M. Santini: "Bi-hamiltonian formulations of the Intermediate LongWave
equation."; Inverse Problems 5, 203 (1989).
[25] P. M. Santini and A. S. Fokas: "The bi-hamiltonian formulations of integrable
evolution equations in multidimensions."; in Proceedings of the
IV Workshop on Nonlinear Evolution Equations and Dynamical Systems;
"Nonlinear evolutions", edited by J.Leon, World Scientific Publishing Company,
Singapore, New Jersey, Hong Kong, 1988.
[26] P. M. Santini: "Dimensional Deformations of Integrable Systems: an
Approach to Integrability in Multidimensions.I"; Inverse Problems 5, 67
(1989).
[27] P. M. Santini: "Old and New Results on the Algebraic Properties of Integrable
Systems in Multidimensions"; in "Some topics on Inverse Problems";
Proceedings of the "XVIth Workshop on Interdisciplinary Study
of Inverse Problems", Montpellier, France, 1987; edited by P.C.Sabatier,
World Scientific, Singapore, 1988.
[28] M. Boiti, F. Pempinelli, F. Calogero and P. M. Santini: "Third Workshop
on Nonlinear Evolution Equations and Dynamical Systems, a short
summary"; Physica 29D, 431 (1988).
[29] A. S. Fokas and P. M. Santini: "Conservation laws for integrable systems";
in "Symmetries and Nonlinear Phenomena"; Procedings of the International
School on Applied Mathematics, Bogota, Colombia; CIF series,
Vol.9. Edited by D.Levi and P.Winternitz. World Scienti c,1988.
[30] P. M. Santini: "The algebraic structures underlying integrability"; Inverse
Problems 6, 99-114 (1990).
[31] P. M. Santini: "Algebraic properties and symmetries of integrable evolution
equations"; in the Proceedings of the Symposium on "Symmetries in Science
III", edited by B.Gruber; Landes-Bildungszentrum, Austria, July 25-28,
1988.
[32] A. S. Fokas and P. M. Santini: "A uni ed approach to recursion operators";
in "Solitons in Physics, Mathematics and Nonlinear Optics", edited
by P.Olver and D.Sattinger, Springer-Verlag, N.Y., 1990.
[33] O. Ragnisco and P. M. Santini: "A Uni ed Algebraic Approach to Integral
and Discrete Evolution Equations"; Inverse Problems 6, 441 (1990).
[34] P. M. Santini: "Solvable nonlinear algebraic equations"; Inverse Problems
6, 665 (1990).
[35] P. M. Santini: "Solvable nonlinear equations as concrete realizations of
the same abstract algebra"; Proceedings Workshop on "Integrable Systems
and Applications", Lecture Notes in Physics, 342; edited by M.Balabane,
P.Lochak, C.Sulem; Springer-Verlag, Berlin, New York, 1988.
[36] A. Degasperis, D. Lebedev, M. Olshanetsky, S. Pakuliak, A. Perelomov and
P. M. Santini; "Nonlocal integrable partners to generalized MKdV and twodimensonal
Toda Lattice equation in the formalism of a Dressing Method
with quantized spectral parameter"; Comm. Math. Phys. 141,133 (1991).
[37] A. Degasperis, D. Lebedev, M. Olshanetsky, S. Pakuliak, A. Perelomov and
P. M. Santini: Generalized intermediate long wave hierarchy in zero curvature
representation with noncommutative spectral parameter; J. Math.
Phys.33, 3783 (1992).
[38] A. S. Fokas and P. M. Santini: "Coherent structures in multidimensions";
Phys.Rev.Lett. 63, 1329 (1989).
[39] A. S. Fokas and P. M. Santini: "Dromions and a Boundary-value Problem
for the Davey- Stewartson Equation; Physica D44, 99 (1990).
[40] P. M. Santini: "Energy exchange of interacting coherent structures in
multidimensions; Physica D41, 26 (1990).
[41] P. M. Santini and A. S. Fokas: "The Initial-Boundary Value Problem for
the Davey- Stewartson I Equation; how to Generate and Drive Localized
Coherent Structures in Multidimensions"; in "Partially Integrable Evolution
Equations in Physics", edited by R.Conte and N.Boccera, NATO ASI
Series, Series C - Vol.310, Kluwer, Dordrecht, 1990.
[42] P. M. Santini and A. S. Fokas: "Solitons and Dromions,coherent structures
in a non linear world"; Proceedings of the V Workshop on "Nonlinear
Evolution Equations and Dynamical Systems"; edited by S.Carillo and
O.Ragnisco; Springer- Verlag, Berlin, 1990.
[43] P. M. Santini and A. S. Fokas: "Dromions, a new manifestation in nonlinear
phenomena", in "Inverse Methods in Action", edited by P.C.Sabatier;
Springer- Verlag, Berlin, 1990.
[44] A. S. Fokas and P. M. Santini: "On the solution of certain systems of
nonlinear algebraic equations"; Preprint INS n.157, Clarkson University,
1990.
[45] B. A. Dubrovin, A. S. Fokas and P.M.Santini: "Spectral theory of linear
l-matrices and the solution of certain nonlinear algebraic and functional
equations"; in Procedings "III Postdam-V Kiev" Workshop, August 1991.
[46] M. Bruschi, O. Ragnisco, P. M. Santini and Tu Guizhang: "Integrable
symplectic maps" Physica D 49, 273 (1990).
[47] M. Bruschi, P. M. Santini and O. Ragnisco: "Integrable cellular automata".
Phys. Letters A 169, 151 (1992).
[48] P. M. Santini: "Integrable nonlinear evolution equations with constraints",
Inverse Problems 8, 285 (1992).
[49] P. M. Santini: "Integrable singular integral evolution equations"; in
"Important Developments in Soliton Theory", edited by A.S.Fokas and
V.E.Zakharov, Springer Verlag (1992).
[50] B. A. Dubrovin, A. S. Fokas and P. M. Santini: "Integrable functional
equations and Algebraic-Geometry; Duke Mathematical Journal 76, 645-
668 (1994).
[51] M. Bruschi and P. M. Santini: "Cellular automata in 1+1, 2+1 and 3+1
dimensions, constants of motion and coherent structures"; Physica D 70,
185-209 (1994).
[52] A. Doliwa and P. M. Santini: "An elementary geometric charaterization of
the integrable motions of a curve"; Phys. Lett. A 185, 373 (1994).
[53] C. Bernardini, O. Ragnisco e P. M. Santini: "Metodi Matematici della
Fisica"; La Nuova Italia Scientifica, 1993.
[54] A. Doliwa and P. M. Santini: "Integrable dynamics of a discrete curve and
the Ablowitz-Ladik hierarchy"; J.Math.Phys. 36, 1259-1273 (1995).
[55] A. Doliwa and P. M. Santini: "The integrable dynamics of discrete curves",
in: "Symmetries and Integrability of Difference Equations"; eds. D. Levi,
L. Vinet and P. Winternitz, CRM Proceedings and Lecture Notes, Vol. 9,
AMS Providence, 1996.
[56] A. Degasperis, S. V. Manakov and P. M. Santini: "Multiple-Scale Perturbation
beyond the Nonlinear Schroedinger Equation. I", Physica D, 100,
187-211 (1997).
[57] P. M. Santini: "Linear Theories, Hidden variables and Integrable Nonlinear
Equations"; Phys. Lett. 212 A, 43 (1996).
[58] P. M. Santini: The Method of the Multiple-Scales and the Nonlinear
Schroedinger Hierarchy", Proceedings of the 1st Workshop "Nonlinear
Physics, Theory and Experiments", Gallipoli (Lecce); edited by E.Alfinito,
M.Boiti, L.Martina and F.Pempinelli, World Scientific, 1996.
[59] P. M. Santini: "Multiscale expansions, symmetries and the nonlinear
Schroedinger hierarchy", in "Algebraic Aspects of Integrable Systems, In
Memory of Irene Dorfman", edited by A.S.Fokas and I.M.Gelfand, Vol. 26,
Birkhauser (Boston), 1996.
[60] M. Manas and P. M. Santini: "Solutions of the Davey - Stewartson II
equation with arbitrary rational localization and nontrivial interaction";
Physics Letters A 227,325-334 (1997).
[61] A. Doliwa and P. M. Santini: "Multidimensional quadrilateral lattices are
integrable"; Physics Letters A 233, 365-372 (1997).
[62] M. Manas, A. Doliwa and P. M. Santini: \Darboux transformations for
multidimensional quadrilateral lattices.I"; Physics Letters A 232, 99-105
(1997).
[63] J. Cieslinski, A. Doliwa and P. M. Santini: "The integrable discrete analogues
of orthogonal coordinate systems are multidimensional circular lattices".
Physics Letters A 235, 480-488 (1997).
[64] A. Doliwa, S. V. Manakov and P. M. Santini: "DBAR - reductions of the multidimensional
quadrilateral lattice I: the multidimensional circular lattice".
Commun. Math. Phys. 196, 1-18 (1998).
[65] A. Doliwa and P. M. Santini: "Geometry of discrete curves and lattices
and integrable difference equations". Published in the book \Discrete Integrable
Geometry and Physics"; editors A. Bobenko and R. Seiler, Oxford
University Press (1999).
[66] A. Doliwa, P. M. Santini and M. Manas: "Transformations of Quadrilateral
Lattices". J. Math. Phys. 41 (2000) 944 - 990.
[67] A. Doliwa, M. Manas, L. Martinez Alonso, E. Medina and P. M. Santini:
"Charged Free Fermions, Vertex Operators and Classical Transformations
of Conjugate Nets". J. Phys. A 32 (1999) 1197-1216.
[68] A. Doliwa and P. M. Santini: "The symmetric, d-invariant and Egorov
reductions of the quadrilateral lattice"; J. Geometry and Physics 36, (2000)
60-102.
[69] A. Doliwa and P. M. Santini: "Integrable Discrete Geometry: The Quadrilateral
Lattice, its Transformations and Reductions"; CRM Proceedings and
Lecture Notes, Volume 25, (2000) 101-119.
[70] A. Doliwa, M. Nieszporski and P. M. Santini: "Asymptotic lattices and
their integrable reductions I: the Bianchi - Ernst and the Fubini - Ragazzi
lattices"; J. Phys. A: Math. and Gen. 34 (2001), 10423-10439.
[71] A. Degasperis, S. V. Manakov and P. M. Santini: "On the initial - boundary
value problems for soliton equations"; JETP Letters, Vol. 74, No. 10,
(2001) 481-485.
[72] A. Degasperis, S. V. Manakov and P. M. Santini: "Initial-boundary value
problems for linear PDEs: the analyticity approach"; in "New trends in
integrability and partial solvability", 79-103 (2004). Edited by A.B.Shabat
et al., Kluwer Academic Publishers. arXiv:nlin.SI/0210058.
[73] A. Degasperis, S. V. Manakov and P. M. Santini: \Initial-boundary value
problems for linear and soliton PDEs"; \NEEDS 2001-Special Issue" of
Theor. Math. Phys., 133: 1475-1489 (2002). arXiv:nlin.SI/0205030.
[74] P. M. Santini: "Transformations and reductions of integrable nonlinear
equations and the DBAR problem"; in: Geometry and Integrability (edited by L.
Mason and Y. Nutku), London Mathematical Society Lecture Notes, vol.
295, Cambridge University Press, 2003.
[75] P. G. Grinevich and P. M. Santini: "The initial - boundary value problem on
the segment for the Nonlinear Schroedinger equation; the algebro-geometric
approach. I". In: Geometry, Topology and Mathematical Physics: S. P.
Novikov Seminar 2001 - 2003, V. M. Buchstaber, I. M. Krichever, editors,
American Mathematical Society Translations, Series 2, Vol. 212, 157-178,
2004. Preprint arXiv:nlin.SI/0307026.
[76] M. Nieszporski, P. M. Santini and A. Doliwa: "Darboux transformations
for 5-point and 7-point self-adjoint schemes and an integrable discretization
of the 2D Schroedinger operator"; Phys. Lett. A. 323 (2004) 241-250.
arXiv:nlin.SI/0307045.
[77] A. Doliwa, M. Nieszporski and P. M. Santini: "Geometric discretization
of the Bianchi system"; Journal of Geometry and Physics. 52 (issue 3),
217-240 (2004). arxiv:nlin.SI/0312005.
[78] M. Nieszporski and P. M. Santini: "The self-adjoint 5-point and 7-point
difference operators, the associated Dirichlet problems, Darboux transformations
and Lelieuvre formulas"; Glasgow Math. J. 47, 1-15 (2005).
arXiv:nlin.SI/0402038.
[79] P. M. Santini, M. Nieszporski and A. Doliwa: "An integrable generalization
of the Toda law to the square lattice"; Physical Review E 70, 1 (2004).
arXiv:nlin/0409050.
[80] A. Doliwa, P. G. 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"; J. Math.
Phys. 48, 013513 (2007). Preprint nlin.SI/0410046.
[81] A. Doliwa and P. M. Santini: "Integrable systems and discrete geometry";
in the Encyclopedia of Mathematical Physics, edited by J.-P. Francoise, G.
Naber and Tsou Sheung Tsun, Oxford: Elsevier, 2006 (ISBN 978-0-1251-
2666-3). http://arXiv.org/abs/nlin/0504041
[82] A. Degasperis, S. V. Manakov and P. M. Santini: "Integrable and nonintegrable
initial-boundary value problems for soliton equations"; JNMP, 12,
Supplement 1, 228-243, 2005.
[83] U. Mugan, A. Sakka, P. M. Santini: "Schlesinger transformations for discrete
Painlevé equation: dPII "; Phys. Lett. A, 336, 37-45, 2005.
[84] F. Calogero, D. Gomez-Ullate, P. M. Santini and M. Sommacal: "The
transition from regular to irregular motion as travel on Riemann surfaces";
J. Phys. A: Math. Gen. 38 (2005) 8873-8896. http://arXiv:nlin.SI/0507024.
[85] S. V. Manakov and P. M. Santini: \Inverse scattering problem for vector
fields and the heavenly equation"; http://arXiv:nlin.SI/0512043.
[86] A. I. Zenchuk and P. M. Santini: \Partially integrable systems in multidimensions
by a variant of the dressing method. 1"; J. Phys. A: Math. Gen.
39 (2006) 5825-5845. http://arXiv:nlin.SI/0512062.
[87] S. V. Manakov and P. M. Santini: \The Cauchy problem on the plane for
the dispersionless Kadomtsev-Petviashvili equation"; JETP Letters, 83,
No 10, 462-466 (2006). http://arXiv:nlin.SI/0604016.
[88] S. V. Manakov and P. M. Santini: "Inverse scattering problem for vector
fields and the Cauchy problem for the heavenly equation"; Phys. Lett. A
359, 613-619 (2006). http://arXiv:nlin.SI/0604017.
[89] P. G. Grinevich and P. M. Santini: "Newtonian dynamics in the plane
corresponding to straight and cyclic motions on the hyperelliptic curve
mu^2 = nu^n-1: ergodicity, isochrony, periodicity and fractals"; Physica
D 232 (2007) 22-32. http://arXiv:nlin.CD/0607031.
[90] S. V. Manakov and P. M. Santini: "A hierarchy of integrable PDEs in 2+1
dimensions associated with 1 - dimensional vector fields"; Theor. Math.
Phys. 152: 1004-1011 (2007). http://arXiv:nlin.SI/0611047
[91] P. M. Santini and A. I. Zenchuk: "The general solution of the matrix
equation w_t+sum w_{x_k}\rho^(k)(w) = \rho(w)+[w; T \tilde\rho(w)]"; Physics
Letters A 368 (2007) 48-52. arXiv:nlin.SI/0612036.
[92] A. I. Zenchuk and P. M. Santini: "Dressing method based on homogeneous
Fredholm equation: quasilinear PDEs in multidimensions"; J. Phys. A:
Math. Theor. 40 (2007) 6147-6174. arXiv:nlin.SI/0701031.
[93] A. Doliwa, M. Nieszporski and P. M. Santini: "Integrable lattices and
their sublattices II. From the B-quadrilateral lattice to the self-adjoint
schemes on the triangular and the honeycomb lattices", JMP 48 113506.
arXiv:0705.0573.
[94] P. M. Santini, A. Doliwa, M. Nieszporski: "Integrable dynamics of Todatype
on the square and triangular lattices", Phys. Rev. E 77, 056601-12 pp
ISSN: 1539-3755 (2008). arXiv:0710.5543.
[95] S. V. Manakov and P. M. Santini: "On the solutions of the dKP equation:
nonlinear Riemann Hilbert problem, longtime behaviour, implicit
solutions and wave breaking", J.Phys.A: Math.Theor. 41 (2008) 055204.
(arXiv:0707.1802 (2007))
[96] A. I. Zenchuk and P. M. Santini: "On the remarkable relations among
PDEs integrable by the inverse spectral transform method, by the method
of characteristics and by the Hopf-Cole transformation". J. Phys. A: Math.
Theor. 41 No 18 185209 (28pp) (2008). arXiv:0801.3945.
[97] F. Calogero, D. Gomez-Ullate, P. M. Santini, M. Sommacal: "Towards a
Theory of Chaos Explained as Travel on Riemann Surfaces", J. Phys. A:
Math. Theor. 42 (2009) 015205 (26pp). arXiv:0805.4130v1 .
[98] S. V. Manakov and P. M. Santini: "The dispersionless 2D Toda equation:
dressing, Cauchy problem, longtime behavior, implicit solutions
and wave breaking", J. Phys. A: Math. Theor. 42 (2009) 095203 (16pp).
doi:10.1088/1751-8113/42/9/095203. ArXiv:0810.4676
[99] S. V. Manakov and P. M. Santini: "On the solutions of the second heavenly
and Pavlov equations", J. Phys. A: Math. Theor. 42 (2009) 404013 (11pp).
doi: 10.1088/1751-8113/42/40/404013. ArXiv:0812.3323.
[100] P. M. Santini, "Multiscale expansions of difference equations in the
small lattice spacing regime, and a vicinity and integrability test. I",
J. Phys. A: Math. Theor. 43 (2010) 045209 (27pp) doi: 10.1088/1751-
8113/43/4/045209 . ArXiv:0908.1492
[101] S. V. Manakov and P. M. Santini: "On the dispersionless Kadomtsev-
Petviashvili equation in n+1 dimensions: exact solutions, the Cauchy problem
for small initial data and wave breaking", ArXiv:1001.2134.