On the Caudrey-Beals-Coifman System and the Gauge Group Action

References

• Ablowitz , M J , Kaup , D J , Newell , A C and Segur , H . 1974 . The inverse scattering transform–Fourier analysis for nonlinear problems . Studies in Appl. Math. , 53 ( 4 ) : 249 – 315 .
   Web of Science ®Google Scholar
• Beals , R and Coifman , R R . 1984 . Scattering and inverse scattering for first order systems . Commun. Pure and Appl. Math. , 37 ( 1 ) : 39 – 90 .
   Web of Science ®Google Scholar
• Beals , R and Coifman , R R . 1985 . Commun. Pure & Appl. Math. , 38 : 29 – 42 .
   Web of Science ®Google Scholar
• Beals , R and Coifman , R R . 1987 . Scattering and inverse scattering for first order systems II . Inverse Problems , 3 : 577 – 594 . Beals R And Coifman R R, Linear spectral problems, nonlinear equations and the delta-method, Inverse Problems 5 (1989), 87–130.
   Google Scholar
• Beals , R and Sattinger , D . 1991 . On the complete integrability of completely integrable systems . Commun. Math. Phys. , 138 : 409 – 436 .
   Web of Science ®Google Scholar
• Bourbaki , N . Éléments de mathématique. Groupes et algèbres de Lie. Chapters I–VIII , 1960 – 1975 . Paris : Hermann .
   Google Scholar
• Caudrey , P J . 1982 . The inverse problem for a general N×N spectral equation . Physica D , D6 : 51 – 66 .
   Google Scholar
• Coxeter , H S M and Moser , W O J . 1972 . Generators and relations for discrete groups , New York , Berlin–Heidelberg : Springer Verlag .
   Google Scholar
• Faddeev , L D and Takhtadjan , L A . 1987 . Hamiltonian approach in the theory of solitons , Berlin : Springer Verlag .
   Google Scholar
• Ferapontov , E V . 1995 . Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and N-wave systems . Diff. Geom. Appl. , 5 : 335 – 369 .
   Google Scholar
• Fordy , A P and Gibbons , J . 1980 . Integrable nonlinear Klein–Gordon equations and Toda lattices . Commun. Math. Phys. , 77 : 21 – 30 .
   Web of Science ®Google Scholar
• Fordy , A P and Kulish , P P . 1983 . Nonlinear Schrödinger equations and simple Lie algebras . Commun. Math. Phys. , 89 : 427 – 443 .
   Web of Science ®Google Scholar
• Gerdjikov , V S . 1994 . The Generalized Zakharov–Shabat System and the Soliton Perturbations . Teor Mat. Fiz. , 99 : 292 – 299 .
   Google Scholar
• Gerdjikov , V S and Kulisx , P P . 1981 . The generating operator for the n×n linear system . Physica D , 3 : 549 – 564 . Gerdjikov V S, Generalized Fourier transforms for the soliton equations. Gauge covariant formulation, Inverse Problems 2 (1986), 51–74.
   Google Scholar
• Gerdjikov , V S , Grahovski , G G and Kostov , N A . 2001 . Reductions of N-wave interactions related to simple Lie algebras I: Z 2-reductions . J. Phys. A: Math. and Gen. , 34 : 9425 – 9461 .
   Google Scholar
• Gerdjikov , V S , Grahovski , G G and Kostov , N A . 2002 . On N-wave type systems and their gauge equivalent . Eur Phys. J. B , 29 : 243 – 248 .
   Google Scholar
• Gerdjikov , V S , Grahovski , G G , Ivanov , R I and Kostov , N A . 2001 . N-wave interactions related to simple Lie algebras. Z 2-reductions and Soliton solutions . Inverse Problems , 17 : 999 – 1015 .
   Google Scholar
• Gerdjikov , V S and Yanovski , A B . 1994 . Completeness of the eigenfimctions for the Caudrey–BealsCoifinan system . J. Math. Phys. , 35 : 3687 – 3725 .
   Google Scholar
• Grahovski , G G . 2002 . “ On The Reductions and Scattering Data for the CBC System ” . In In “Geometry, Integrability and Quantization III” , Edited by: Mladenov , I and Naber , G . 262 – 277 . Sofia : Coral Press .
   Google Scholar
• Goto , M and Grosshans , F . 1978 . Semisimple Lie algebras, Lecture Notes in Pure and Applied Mathematics , Edited by: Dekker , M. Vol. 38 , New York : Basel .
   Google Scholar
• Helgasson , S . 1978 . Differential geometry, Lie groups and symmetric spaces , Academic Press .
   Google Scholar
• Humphreys , J E . 1990 . Reflection Groups and Coxeter Groups , Cambridge : Cambridge University Press .
   Google Scholar
• Ivanov , R I . 2004 . On the dressing method for the generalised Zakharov-Shabat system . Nuclear Physics B , 694 : 509 – 524 .
   Google Scholar
• Mikhailov , A V . 1981 . The reduction problem and the inverse scattering problem . Physica D , 3 : 73 – 117 .
   Google Scholar
• Mikhailov , A V , Olshanetzky , M A and Perelomov , A M . 1981 . Two-dimensional generalized Toda lattice . Commun. Math. Phys. , 79 : 473 – 490 .
   Google Scholar
• Reyman , A G . 1983 . An unified Hamiltonian system on polynomial bundles and the structure of the stationary problems . Zap. Nauch. Semin. , : 118 – 127 . LOMI131 (In Russian)
   Google Scholar
• Zakharov , V E and Manakov , S V . 1975 . Exact theory of resonant interaction of wave packets in nonlinear media , 74 – 41 . Novosibirsk : INF preprint . (In Russian)
   Google Scholar
• Zakharov , V E , Manakov , S V , Novikov , S P and Pitaevskii , L I . 1984 . Theory of solitons. The inverse scattering method , N.Y : Plenum .
   Google Scholar
• Zakharov , V E and Mikhailov , A V . 1980 . On the integrability of classical spinor models in two-dimensional space-time . Commun. Math. Phys. , 74 : 210
   Google Scholar
• Zakharov , V E and Shabat , A B . 1971 . Exact theory of two-dimensional selffocusing and one-dimensional automodulation in nonlinear media . Zh. Exp. Teor Fiz. , 61 : 118 – 134 .
   Google Scholar
• Zhou , X . 1989 . Direct and inverse scattering transform with arbitrary spectral singularities . Commun. Pure & Appl. Math. , 42 : 895 – 938 .
   Web of Science ®Google Scholar
• Zakharov , V E and Takhtajan , L A . 1979 . The equivalence between the nonlinear Schrödinger equation and the Heisenberg ferromagnet equation . Teor Mat. Fiz. , 38 : 35
   Google Scholar