Abstract
In recent years many progresses have been made in the comprehension of the rich mathematical structure of nonlinear integrable systems, which very often turn out to be relevant in the description of natural phenomena1).
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References
F.Calogero and A.Degasperis,Spectral Transform an Solitons I, Studies in Mathematics and its Applications, North-Holland Publishing Company, Amsterdam,1982.
M.Ablowitz and H.Segur,Solitons and the Inverse Scattering Transform,in SIAM Studies in Applied Mathematics, No.4 CSIAM,Philadelphia,1981.
S.Novikov, S.V.Manakov, L.P.Pitaevskii and V.E.Zakharov, Theory of Solitons, The Inverse Scattering Method, Contemporary Soviet Mathemaics, Consult ants Bureau. New York and London,1984.
P.M.Santini and A.S.Fokas,Recursion operators and bi-hamiltonian structures in multidimensions I, Comm.Math.Phys.115, 375 (1988).
A.S.Fokas and P.M.Santini, Recursion operators and bi-hamiltonian structures in multidimensions II, Comm.Math.Phys.116, 449 (1988).
P.M.Santini and A.S.Fokas, The bi-hamiltonian formulations of integrable evolution equations in multidimensions, in Nonlinear Evolutions, Proceedings of the IV Workshop on Nonlinear Evolution Equations and Dynamical Systems; edited by J.Leon, World Scientific Publishing Company, Singapore (1988).
P.M.Santini, Dimensional deformations of integrable systems, an approach to integrability in multidimensions.I, Preprint 586 Dipartimento di Fisica, Universita’ di Roma I,1988; Inverse Problems (submitted to).
A.S.Fokas and P.M.Santini, Stud.Appl.Math.75, 179 (1986).
A.S.Fokas and P.M.Santini, J.Math.Phys.29, 604 (1988).
M.Bruschi, private communication.
A.S.Fokas and B.Fuchssteiner, Phys.Lett.86A, 341 (1981).
W.Oevel and B.Fuchssteiner,Phys.Lett.88A, 323 (1982).
H.H.Chen, Y.C.Lee and J.E.Lin, Physica9D, 439 (1983).
B.Fuchssteiner, Progr.Theoret.Phys.70,150 (1983).
B.G.Konopelchenko, Recursion and group theoretical structures of the integrable equations in 1+1 and 2+1 dimensions. Bilocal approach, Preprint INP Novosibirsk, USSR, 1987.
S.V.Manakov : private communication. A.S.Fokas, Phys.Rev.Lett.57, 159 (1986).
F.Calogero, Lett. Nuovo Cimento14, 443, (1975).
F.Calogero, Lett.Nuovo Cimento14, 537 (1975);
F.Calogero and A.Degasperis, Nuovo Cimento32B, 201 (1976);
F.Calogero and A.Degasperis, Nuovo Cimento39B, 1 (1977)
M.Bruschi, D.Levi and O.Ragnisco, Lett.Nuovo Cimento33, 263 (1982).
M.Bruschi, D.Levi and O.Ragnisco, Phys.Lett.88A, 379 (1982).
We thank W.Craig for showing us that equation (4.16) can be integrated using the method of the characteristics.
P.M.Santini, Bi-hamiltonian formulations of the Intermediate Long Wave equation,Preprint INS 80,Clarkson University,1987;Inverse Problems (submitted to).
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© 1989 Plenum Press, New York
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Santini, P.M. (1989). Algebraic Properties and Symmetries Of Integrable Evolution Equations. In: Gruber, B., Iachello, F. (eds) Symmetries in Science III. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0787-7_26
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DOI: https://doi.org/10.1007/978-1-4613-0787-7_26
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