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Prog. Theor. Phys. Vol. 74 No. 5 (1985) pp. 1005-1012
Recursion Operators for N×N Matrix Nonlinear Evolution Equations
Naruyoshi Asano and
Yusuke Kato
Department of Engineering Mathematics, Utsunomiya University, Utsunomiya 321
(Received June 22, 1985)
Abstract:
In the Ablowitz-Kaup-Newell-Segur theory for N×N matrix systems, the associated general nonlinear evolution equation is obtained, in which the recursion operator is directly derived from the integrability condition. Discussed are also the nonlinear superposition law and symmetries associated with the evolution equations.
URL :
http://ptp.ipap.jp/link?PTP/74/1005/
DOI : 10.1143/PTP.74.1005
References:
- M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Stud. Appl. Maths. 53 (1974), 249.
- B. G. Konopelchenko, Phys. Lett. 108B (1982), 26.
- A. C. Newell, Nonlinear Evolution Equations Solvable by the Spectral Transform (Pitman, 1978), p. 127.
- N. Asano and Y. Kato, Prog. Theor. Phys. 58 (1977), 161[PTP].
- B. Fuchssteiner, Nonlinear Anal. Theory Meth. Appl. 3 (1979), 849.
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P. J. Olver, J. Math. Phys. 18 (1977), 1212[CrossRef].
- R. Beals and R. R. Coifman, Comm. Pure Appl. Math. 37 (1984), 39.
- Y. Kato and H. Nakajima, in preparation.
- A. B. Shabat, Funk. Anal. Pril. 9 (1975), 75.
- V. S. Gerdjikov, Lett. Math. Phys. 6 (1982), 315.
Citing Article(s) :
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Progress of Theoretical Physics Vol. 76 No. 5 (1986) pp. 981-998
:
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Spectral Problem of N ×N Matrix Differential Operators on the Line
-
Yuseke Kato and Hideo Nakajima
-
Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 198-213
:
-
Fredholm Determinants and the Cauchy Problem of a Class of Nonlinear Evolution Equations
-
Yusuke Kato
-
Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 774-792
:
-
The Marchenko Equation of the Hilbert-Schmidt Type for the N ×N Zakharov-Shabat Operator
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Naruyoshi Asano and Yusuke Kato
