Trace identities in the inverse scattering transform method associated with matrix Schrödinger operators
| dc.contributor.author | Martínez Alonso, Luis | |
| dc.contributor.author | Olmedilla Moreno, Eugenio | |
| dc.date.accessioned | 2023-06-21T02:09:15Z | |
| dc.date.available | 2023-06-21T02:09:15Z | |
| dc.date.issued | 1982 | |
| dc.description | ©1982 American Institute of Physics. | |
| dc.description.abstract | Trace identities arising in the scattering theory of one-dimensional matrix Schrodinger operators are deduced. They derive from the properties of an asymptotic expansion of the trace of the resolvent kernel in inverse powers of the spectral parameter. Applications of these trace identities for characterizing infinite families of conservation laws for nonlinear evolution equations are given. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/33074 | |
| dc.identifier.doi | 10.1063/1.525265 | |
| dc.identifier.issn | 0022-2488 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1063/1.525265 | |
| dc.identifier.relatedurl | http://scitation.aip.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64992 | |
| dc.issue.number | 11 | |
| dc.journal.title | Journal of mathematical physics | |
| dc.language.iso | eng | |
| dc.page.final | 2121 | |
| dc.page.initial | 2116 | |
| dc.publisher | American Institute of Physics | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Physics | |
| dc.subject.keyword | Mathematical | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Trace identities in the inverse scattering transform method associated with matrix Schrödinger operators | |
| dc.type | journal article | |
| dc.volume.number | 23 | |
| dcterms.references | 1.L. D. Faddeev and V. E. Zakharov, Funkcional Anal. Prilozen. 5, 18 (1971). 2.V. E. Zakharov and S. V. Manakov, Theor. Math. Phys. 19, 332 (1974). 3.L. D. Faddeev and L. A. Takhtajan, Theor. Math. Phys. 21, 160 (1974). 4.L. D. Faddeev and V. E. Korepin, Phys. Rep. 42,1 (1978). 5.L. D. Faddeev, "A Hamiltonian Interpretation of the Inverse Scattering Method" in Solitons, edited by R. K. Bullough and P. J. Caudrey (Springer, Berlin, 1980). 6. See the references quoted in the article by M. Fowler, "The Quantum Inverse Scattering Method and Applications to Spin Chains" in Physics in One Dimension, edited by J. Bernasconi and T. Schneider, Springer Series in Solid-State Sciences, Vol. 23 (Springer, Berlin, 1981). 7.M. Wadati and T. Kamijo, Prog. Theor. Phys. 52, 397 (1974). 8.F. Calogero and A. Degasperis, Nuovo Cimento B 39, 1 (1977). 9.I. M. Gel'fand and L. A. Diki, Usp. Math. Nauk 30, 67 (1975); Funkcional Anal. Prilozen. 10,18 (1976); Funkcional Anal. Prilozen. 10,13 (1976); Funkcional Anal. Prilozen. II, 11 (1977); Funkcional Anal. Prilozen. 12, 8 (1978). 10.L. D. Faddeev, Trudy Mat. Inst. Steklov 73,314 (1964). 11.P. Deift and E. Trubowitz, Comm. Pure Appl. Math. 32, 121 (1979). 12.ǀThis condition is more suitable than the usual one, (1 + ǀxǀ) ǀV ǀε L '(R), in order to characterize the behavior of the scattering coefficients at k = O. See Ref. 11. 13.The bounds for F + and F + (respectively, F _ and F _) are uniform with respect to x in the intervals (-ß ∞, 00) [respectively, ( - ∞, ß)], where α, ß are arbitrary finite numbers. 14.0. Ragnisco, Lett. Nuovo Cimento 31,651 (1981). 15.E. Olmedilla, L. Martinez Alonso, and F. Guil, Nuovo Cimento B 61, 49 (1981). 16.See the proof of Lemma 6 of Ref. 11. Similar arguments lead to (3.8a) and (3.8b). I7.E. F. Beckenbach, Bull. Amer. Math. Soc. 49, 615 (1943). 18.See part V of Theorem 1 of Ref. 11. The statement remains true for the matrix case. 19.See Part IV of Theorem 1 of Ref. 11. 20.A. Degasperis, "Spectral Transform and Solvability of Nonlinear Evolution Equations" in Nonlinear Problems in Theoretical Physics, edited by A. F. Raiiada, Lecture Notes in Physics, Vol. 98 (Springer, Berlin, 1979). 21 A. C. Newell, "The Inverse Scattering Method" in Solitons, edited by R. K. Bullough and P. J. Caudrey (Springer, Berlin, 1980). 22M. Wadati, "Generalized Matrix Form of the Inverse Scattering Meth• od" in Solitons, edited by R. K. Bullough and P. J. Caudrey (Springer, Berlin, 1980). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 896aafc0-9740-4609-bc38-829f249a0d2b | |
| relation.isAuthorOfPublication | c92f38f0-bc01-4d8e-8079-b273f94ac59f | |
| relation.isAuthorOfPublication.latestForDiscovery | 896aafc0-9740-4609-bc38-829f249a0d2b |
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